! In the title line, the ODE, it should be  omega_0 , not omega_n.
! (Math standard would write omega_0^2  with the 2 directly above the 0,
! by the way, but this isn't too important.)
! Check subscripts with Haynes !!!

! Dennis Zill on damping

! mx'' + Bx' + kx = 0  where  B is a positive damping constant
! x'' + B/m x' + k/m x = 0
! or
! x'' + 2Z x' + w^2 x = 0  where  2Z = B/m  and  w^2 = k/m
! engineers call this w the natural frequency, w_n
! 2Z is used for convenience to make the auxiliary equation
! m^2 + 2Zm + w^2 = 0
! the roots of this equation are

! m1 = (-2Z + sqrt((2Z)^2 - 4w^2)) / 2
! m2 = (-2Z - sqrt((2Z)^2 - 4w^2)) / 2

! m1 = (-2Z + sqrt(4Z^2 - 4w^2)) / 2
! m2 = (-2Z - sqrt(4Z^2 - 4w^2)) / 2

! m1 = (-2Z + 2sqrt(Z^2 - w^2)) / 2
! m2 = (-2Z - 2sqrt(Z^2 - w^2)) / 2

! m1 = -Z + sqrt(Z^2 - w^2)
! m2 = -Z - sqrt(Z^2 - w^2)

! Z = B/(2m)  and  w = sqrt(k/m)
! if Z^2  = w^2          damping is critical
! if Z    = w            damping is critical
! if B/2m = sqrt(k/m)    damping is critical
! if B    = 2m sqrt(k/m) damping is critical

! 2m sqrt(k/m) is the value of critical damping


! x'' + 2Z w_n x' + w_n^2 x = 0
! w_n = sqrt(k/m)  and  2Z  = B/m
! x'' + B/m sqrt(k/m) x' + k/m x = 0



!! File: Damping Ratio
!! May 26, 2003 Hubert Hohn

PUBLIC PCFlag,Mac5Flag,M68KFlag,UnixFlag,xmax,ymax
PUBLIC toolLft,toolRgt,toolBas,toolTop,toolhdr,toolHgt,toolWid  ! tool boundaries
PUBLIC winLft,winRgt,winBas,winTop,winHgt,winWid      ! window
PUBLIC workLft,workRgt,workBas,workTop,workMidx  ! work area
PUBLIC backclr,black,drkgry,drkmid,midgry,litmid,litgry,white
PUBLIC red,yellow,green,cyan,blue,magenta,pink,colorscheme
PUBLIC planeclr,gridclr,rimclr,axisclr,axislabelclr,titleclr,rightsclr
PUBLIC numberlineclr,slotdrkclr,slotlgtclr,slideclr
PUBLIC largefonts, title$, SLUmode

LET toolHgt= 560
LET toolWid= 780
LET window$= "The d'Arbeloff Interactive Math Project"

LET title$ = "The Damping Ratio"

SUB ThisProgram
    CALL DampingRatio
    CLEAR
END SUB


!! ---------------------------------------------------------
!! ------ Start TB4 Mac Header and Subs ------

!LET M68KFlag = 1
!LIBRARY "MacTools*", "HHLib.trc"
!ASK PIXELS winWid,winHgt
!LET winLft= 0
!LET winTop= 0
!LET winRgt= winWid-1
!LET winBas= winHgt-1
!SET WINDOW 0,winRgt,winBas,0
!CALL Palette
!CLEAR
!
!CALL ToolPanel
!CALL ThisProgram
!
!END
!EXTERNAL
!
!MODULE Mac4Parts
!    SUB SetTextFont(font,size,style$)
!        CALL MacTextFont(font)
!        CALL MacTextSize(size)
!        CALL MacTextFace(style$)
!    END SUB
!
!    SUB StringWidth(sw$,sl)
!        DECLARE DEF MacStringWidth
!        LET sl= MacStringWidth(sw$)
!    END SUB
!
!    SUB SetLineWeight(wgt)
!        CALL MacPenSize(wgt,wgt)
!    END SUB
!
!    SUB BoxDisk(Lft,Rgt,Bas,Top)
!        CALL MacPaintOval(Lft,Rgt,Bas,Top)
!    END SUB
!END MODULE

!! --- End TB4 Mac Header and Subs ---
!!---------------------------------------------------------
!!--- Start TB5 Cross-Platform header and subs ---

LIBRARY "c:\TB Gold 51a\TBLibs\TrueCtrl.trc"     ! windows
LIBRARY "c:\TB Gold 51a\TBLibs\HHLib.trc"

!LIBRARY ":TBLibs:TrueCtrl.trc"                   ! macintosh
!LIBRARY "HHLib.trc"

PUBLIC WinID
DECLARE PUBLIC OBJM_SET,OBJM_SYSINFO
LET winHgt= toolHgt
LET winWid= toolWid
DIM values(1)

CALL TC_Init

CALL Object(OBJM_SYSINFO,WinID,"MACHINE",system$,values())
IF system$="MAC" then
   LET Mac5Flag= 1
ELSE IF system$="WIN32" then
   LET PCFlag  = 1
END IF

CALL TC_SetUnitsToPixels                         ! 5.1 and up needs this
CALL TC_GetScreenSize(scrnLft,scrnRgt,scrnBas,scrnTop)
LET winLft= int((scrnRgt-scrnLft-winWid)/2)
LET winRgt= winLft+winWid-1
LET winTop= int((scrnBas-scrnTop-winHgt)/2) + 10
LET winBas= winTop+winHgt-1

CALL TC_Win_Create (WinID,"TITLE",winLft,winRgt,winBas,winTop)
LET values(1)= 2
CALL Object(OBJM_SET, WinID, "TYPE", "", values())

IF PCFlag=1 then                                 ! kill dithering
   LET  values(1)= 1
   CALL Object(OBJM_SET, WinID, "SOLID MIX", "", values())
END IF

LET  values(1)= 0
CALL TC_SetRect(WinID,winLft,winRgt,winBas,winTop)
CALL TC_Win_SetTitle(WinID,window$)
CALL TC_Show(WinID)

SET MODE "COLORSTANDARD"

ASK PIXELS winWid,winHgt                         ! must follow set mode
LET winLft= 0
LET winTop= 0
LET winRgt= winWid-1
LET winBas= winHgt-1
SET WINDOW 0,winRgt,winBas,0

CALL Palette

IF PCFlag=1 then
   LET  values(1)= 0                             ! now force solid colors
   CALL Object(OBJM_SET, WinID, "SOLID MIX", "", values())
   CALL TC_Win_RealizePalette(WinID)             ! some PCs need this

   CALL TC_Win_SetFont(WinID,"arial",9,"plain")
   CALL StringWidth("0",sw)
   IF sw>7 then LET largefonts=1 else LET largefonts=0
END IF

CALL TC_Win_Switch(WinID)

CALL ToolPanel
CALL ThisProgram

CALL SetTextFont(1,12,"bold")                    ! now shut down and clean up
LET quit$= "click the mouse or press x0 key to close..."
CALL PlotTextCJ(workmidx,(workbas+worktop)/2,quit$,yellow)
CALL TC_CleanUp

END
EXTERNAL

MODULE TB5Parts
    SUB StringWidth(sw$,sl)
        DECLARE PUBLIC WinID
        LET sl= StrWidth(WinID,sw$)
    END SUB

    SUB SetLineWeight(wgt)
        DECLARE PUBLIC OBJM_SET
        DECLARE PUBLIC WinID
        DIM values(1)
        LET values(1)= wgt
        CALL Object(OBJM_SET,WinID, "WIDTH", "", values())
    END SUB

    SUB SetTextFont(font,size,style$)
        DECLARE PUBLIC WinID,Mac5Flag,PCFlag,largefonts
        IF Mac5Flag=1 then
           SELECT CASE font
           CASE 4
                LET font$= "Courier"
           CASE 16
                LET font$= "Times"
           CASE else
                LET font$= "Geneva"
           END SELECT
        ELSE IF PCFlag=1 then
           IF largefonts=1 then
              IF size<12 then
                 LET size=  6
              ELSE IF size=14 then
                 LET size= 10
              ELSE IF size=18 then
                 LET size= 12
              ELSE IF size=24 then
                 LET size= 14
              ELSE IF size=12 then
                 LET size=  8
              ELSE
                 LET size= round(72/96 * size * .8)
              END IF
           ELSE
              IF size<12 then
                 LET size=  7
              ELSE IF size=14 then
                 LET size= 12
              ELSE IF size=12 then
                 LET size=  9
              ELSE IF size=18 then
                 LET size= 14
              ELSE IF size=24 then
                 LET size= 18
              ELSE
                 LET size= round(72/96 * size)
              END IF
           END IF
           SELECT CASE font
           CASE 4
                LET font$= "Courier New"
           CASE 16
                LET font$= "Times New Roman"
           CASE else
                LET font$= "Verdana"
           END SELECT
        END IF
        IF style$= "normal" then LET style$= "plain"
        CALL TC_Win_SetFont(WinID,font$,size,style$)
    END SUB

    SUB BoxDisk(Lft,Rgt,Bas,Top)
        BOX DISK Lft,Rgt,Bas,Top
    END SUB
END MODULE

!  --- End TB5 Cross-platform header and subs ---
!! ---------------------------------------------------------

!! --- Start Unix Header and Subs ---

!library "HHLib.unix"
!LET UnixFlag= 1
!ASK PIXELS winWid,winHgt
!LET winLft= 0
!LET winTop= 0
!LET winRgt= winWid-1
!LET winBas= winHgt-1
!SET WINDOW 0,winRgt,winBas,0
!CALL Palette
!
!CALL ToolPanel
!CALL ThisProgram
!
!END
!EXTERNAL
!
!MODULE UnixParts
!    SHARE CharWidth
!
!    SUB SetTextFont(font,size,style$)
!        LET font$= "-adobe-courier-"
!        IF style$= "normal" then
!           LET style$= "medium-r-normal--"
!        ELSE
!           LET style$= "bold-r-normal--"
!        END IF
!        IF size=9 then
!           LET size$= str$(10)
!        ELSE
!           LET size$= str$(size)
!        END IF
!        LET test= SetFont(font$&style$&size$&"*")
!
!        IF size=9 then
!           LET CharWidth=  6
!        ELSE IF size=12 then  ! numeric output - axis labels
!           LET CharWidth=  7
!        ELSE IF size=14 then  ! rare
!           LET CharWidth=  8
!        ELSE IF size=18 then  ! rare
!           LET CharWidth= 10
!        END IF
!    END SUB
!
!    SUB StringWidth(sw$,sl)                      ! string width in pixels
!        ! LET sl= StrWidth(sw$)
!        LET chars= len(sw$)
!        LET sl   = chars*CharWidth
!    END SUB
!
!    SUB SetLineWeight(wgt)
!        ! CALL PenSize(wgt,wgt)
!    END SUB
!
!    SUB BoxDisk(Lft,Rgt,Bas,Top)
!        CALL Fill_Circle(Lft,Rgt,Bas,Top)
!    END SUB
!END MODULE

!! ------ End of TB Unix Header and Subs ------
! -----------------------------------------------------------

MODULE Zeta
    SHARE Zeta(0:12,0:7)
    SHARE thetawid
    LET thetawid= 8

    MAT READ Zeta
    DATA 1,1,0,1,1,1,1,0
    DATA 0,1,1,1,0,0,1,1
    DATA 0,1,1,0,0,0,1,1
    DATA 0,1,1,1,1,1,1,0
    DATA 1,1,0,0,0,0,0,0
    DATA 1,1,0,0,0,0,0,0
    DATA 1,1,0,0,0,0,0,0
    DATA 1,1,0,0,0,0,0,0
    DATA 1,1,0,0,0,0,0,0
    DATA 0,1,1,1,1,0,0,0
    DATA 0,0,0,0,1,1,0,0
    DATA 0,0,0,0,1,1,0,0
    DATA 0,0,1,1,1,0,0,0

    SUB SwapZeta(lft,bas,t$,c$,clr)
        LET l= len(t$)
        LET x= lft
        FOR i= 1 to l
            LET ch$= t$(i:i)
            IF ch$=c$ then
               CALL DrawZeta12(x+1,bas,clr)
               LET x= x+thetawid+1
            ELSE
               CALL PlotTextLJ(x,bas,ch$,clr)
               CALL StringWidth(ch$,sw)
               LET x= x+sw
            END IF
        NEXT i
    END SUB

    SUB DrawZeta12(lft,bas,clr)
        SET COLOR clr
        LET top= bas-9
        FOR row= 0 to 12
            LET wy= top+row
            FOR col= 0 to 7
                LET bit= Zeta(row,col)
                IF bit=1 then
                   LET wx= lft+col
                   PLOT wx,wy
                END IF
            NEXT col
        NEXT row
    END SUB
END MODULE


! ***

SUB DampingRatio
    DECLARE PUBLIC black,drkgry,drkmid,midgry,litmid,litgry,white
    DECLARE PUBLIC red,yellow,green,cyan,blue,magenta,colorscheme
    DECLARE PUBLIC axislabelclr,slideclr,true,false
    DECLARE PUBLIC workLft,workRgt,workBas,workTop,workMidx

    DECLARE DEF quitWithin,infoWithin

    ! --- colors ---

    LET waveclr = cyan
    LET rootclr = yellow
    LET zetaclr = green
    LET ivclr   = white


    ! --- help screen array ---

    ! mx'' + c_vx' + kx = 0
    ! where c_v means viscous damping
    ! x'' + c_v/m x' + k/m x = 0
    ! c_c = 2m sqrt(k/m) = 2mw_n   ! critical damping

    ! to simplify the solutions
    ! w_n = sqrt(k/m)   ! natural frequency
    ! c_c = 2msqrt(k/m) = 2mw_n   ! critical damping
    ! z   = c_v / c_c   ! damping ratio
    ! z   = c_v / 2mw_n
    ! b   = 2 * w_n * c_v / 2mw_n = c_v/m

    !  Damping ratio
    !  
    !  Set the initial conditions on the window at lower left or using the sliders.
    !  
    !  Set the undamped natural circular frequency  omega_n  using the slider at lower 
    !  right.
    !  
    !  Set the damping ratio  zeta  using the slider at bottem center (which actually
    !  reads out the negative of zeta).
    !  The characteristic polynomial is displayed symbolically at right, and its roots
    !  are displayed in yellow and also represented by yellow diamonds in the window
    !  at bottom center. The green dot in that window is the value of  - zeta.
    !  
    !  Buttons control the vertical scale of the right hand graphing window.
    !  The solution is displayed in blue on that window. 
    !  Crosshairs show when you roll the cursor over the right hand window,
    !  and the values of  t  and  x  are displayed.

    DIM info$(1:12)
    MAT READ info$

    DATA "The Damping Ratio"
    DATA ""
    DATA "This tool supports exploration of the effects of the damping ratio, zeta, upon the solution."
    DATA ""
    DATA "The solution is displayed in the time series plane."

    DATA "The numerical buttons set the vertical scale of time series plane."
    DATA "Roll the mouse cursor over the time series plane to display the values of  t  and  x."
    DATA ""
    DATA "To set the initial conditions, click or drag the mouse in the lower left initial value plane or use the initial value sliders."
    DATA "Click or drag the omega_[n] slider to set the undamped natural frequency."
    DATA "Click or drag the -zeta slider to set the negative of the damping ratio. The green dot in the complex plane shows the value of -zeta graphically."

    DATA "The characteristic polynomial is displayed symbolically at right, and its roots are displayed in yellow and are represented by yellow diamonds in the complex plane."


    !  Set the initial conditions on the window at lower left or using the sliders.
    !  
    !  Set the undamped natural circular frequency  omega_n  using the slider at lower 
    !  right.
    !  
    !  Set the damping ratio  zeta  using the slider at bottem center (which actually
    !  reads out the negative of zeta).
    !  The characteristic polynomial is displayed symbolically at right, and its roots
    !  are displayed in yellow and also represented by yellow diamonds in the window
    !  at bottom center. The green dot in that window is the value of  - zeta.
    !  
    !  Buttons control the vertical scale of the right hand graphing window.
    !  The solution is displayed in blue on that window. 

    ! DATA
    ! : LET Z = damping coefficient / critical damping"

    !    DATA ""
    !    DATA "if"
    !    DATA "-mx'' + b x' + kx = 0"
    !    DATA "then"
    !    DATA "-x'' + b/m x' + k/m x = 0"
    !    DATA "if  Z = 1/2 B/m  and  w0 = sqrt(k/m)  then"
    !    DATA "-x'' + 2Zw0 x' + w0^2 x = 0"
    !    DATA "the auxiliary equation becomes:"
    !    DATA "-s^2 + 2Zw0 s + w0^2 = 0"
    !    DATA "and the corresponding roots are:"
    !    DATA "-r1 = -Zw0 + w0 sqrt(Z^2 - 1) i"
    !    DATA "-r2 = -Zw0 - w0 sqrt(Z^2 - 1) i"
    !    DATA ""
    !    DATA "When Z^2-1 > 0 the system is overdamped. The roots are real and there is no oscillation. The position of the mass crosses the axis at most once."
    !    DATA "When Z^2-1 = 0 the system is critically damped. There is one real root and no oscillation. A very slight decrease in damping produces oscillation."
    !    DATA "When Z^2-1 < 0 the system is underdamped. The roots are complex conjugate and the motion is oscillatory."


    ! ---------- Utility functions ---

    DECLARE DEF clamp,roundn,e


    ! ------------ functions -----------

    ! x" + 2 zeta w0 x' + w0^2 x = f(t)"  ! DE
    !	s^2 + 2 zeta w0 s + w0^2            ! characteristic equation
    ! r1 = -Zw0 + w0 sqrt(Z^2 - 1) i      ! roots
    ! r2 = -Zw0 - w0 sqrt(Z^2 - 1) i
    ! w0 is sqrt(k/m)                     ! natural frequency

    SUB SetConstants
        LET z2  = z*z
        LET zw  = z*w
        IF abs(z)<=1 then
           LET sqz2= sqr(1-z2)
        ELSE
           LET d   = sqr(z^2-1)
        END IF
        LET wn = w*sqz2
    END SUB

    DEF fu(t)                                    ! under damped
        IF w=0 then                              ! linear
           LET fu= v0*t + x0
        ELSE
           LET wnt = wn*t
           LET swnt= sin(wnt)
           LET ezwt= exp(-zw*t)
           LET c   = ezwt * (cos(wnt) + (z/sqz2)*swnt)
           LET s   = (ezwt*swnt) / wn
           LET fu  = x0*c + v0*s
        END IF
    END DEF

    DEF fc(t)                                    ! critical damping
        IF w=0 then                              ! linear
           LET fc= v0*t + x0
        ELSE
           LET wt  = w*t
           LET ezwt= exp(-wt)
           !           LET ezwt= exp(-z*wt) ! needed if z can be -1
           !           IF z=1 then
           !              LET c= (1+wt) * ezwt
           !           ELSE IF z=-1 then
           !              LET c= (1-wt) * ezwt
           !           END IF
           LET c = (1+wt) * ezwt
           LET s = t * ezwt
           LET fc= x0*c + v0*s
        END IF
    END DEF

    DEF fo(t)                                    ! over damped
        IF w=0 then                              ! linear
           LET fo= v0*t + x0
        ELSE
           LET d = sqr(z^2-1)
           IF d<>0 then
              LET zd = z/d
              LET wd = 1/(w*d)
              LET wt = w*t
              LET a  = 0.5*((1 + zd)*x0 + wd*v0)
              LET b  = 0.5*((1 - zd)*x0 - wd*v0)
              LET fo = a*exp((-z+d)*wt) + b*exp((-z-d)*wt)
           END IF
        END IF
    END DEF

    DEF env(t) = x0*exp(-zw*t)/sqr(1-z^2)

    SUB Roots(real,imag,im1,im2)
        LET real= -z
        WHEN error in
             LET imag = sqr(1-z*z)
        USE
        END WHEN
        LET im1 =  imag
        LET im2 = -imag
    END SUB

    SUB RealRoots(r1,r2)
        IF z=1 then
           LET r1,r2 = -1
        ELSE
           LET d  = sqr(z^2-1)
           LET r1 = (-z + d)
           LET r2 = (-z - d)
        END IF
    END SUB

    !Steve's equations
    !LET e= exp(1)
    !DEF fc(z,t)= (1+t)*e^(-t)                        ! critical damping
    !DEF fo(z,t)                                      ! over damped
    !    LET sqrt= sqr(z*z-1)
    !    LET t1  = 0.5*(1+z/sqrt) * exp[(-z+sqrt)*t]
    !    LET t2  = 0.5*(1-z/sqrt) * exp[(-z-sqrt)*t]
    !    LET fo  = t1+t2
    !END DEF
    !DEF fu(z,t)                                      ! under damped
    !    LET sqrt= sqr(1-z*z)
    !    LET fu  = e^(-z*t)*[cos(sqrt*t)+z/sqrt*sin(sqrt*t)]
    !END DEF


    ! ---------- Graphing plane parameters and methods ----------

    ! -------------------- w1 plane - time series -----------------------

    ! --- w1 plane data ---

    DECLARE PUBLIC w1Lft,w1Rgt,w1Bas,w1Top,w1Midx,w1Midy
    DECLARE PUBLIC w1fLft,w1fRgt,w1fBas,w1fTop,w1x0,w1y0
    DECLARE PUBLIC w1xFirst, w1xSTik, w1xLTik, w1xLabel, w1xGridstep
    DECLARE PUBLIC w1yFirst, w1ySTik, w1yLTik, w1yLabel, w1yGridstep
    DECLARE PUBLIC w1wWid,w1wHgt,w1fWid,w1fHgt
    DECLARE PUBLIC w1fxRatio,w1fyRatio,w1wxRatio,w1wyRatio,w1Aspect
    DECLARE PUBLIC w1xPiFlag, w1xMult, w1yPiFlag, w1yMult

    LET w1Flag   = 1
    LET w1xPiFlag= 1
    LET w1xMult  = pi
    LET w1yPiFlag= 0
    LET w1yMult  = 1

    LET w1Lft = workMidx - 310                   ! pixel bounds
    LET w1Rgt = w1Lft + 640
    LET w1Top = workTop + 30
    LET w1Bas = w1Top + 200

    LET w1fLft=  0                               ! function bounds * pi
    LET w1fRgt=  8
    LET w1fTop=  1
    LET w1fBas= -1

    LET w1xGridstep= 0                           ! horizontal grid intervals
    LET w1yGridstep= 0                           ! vertical grid intervals

    LET w1xAx$= "t"                              ! axis labels
    LET w1yAx$= "x"

    LET w1xSTik = 0.25                           ! horizontal axis Tik marks
    LET w1xLTik = 0.50
    LET w1xLabel= 1
    LET w1xFirst= w1fLft

    LET w1ySTik = 0.1                            ! vertical axis Tik marks
    LET w1yLTik = 0.5
    LET w1yLabel= 0.5
    LET w1yFirst= w1fBas

    ! --- w1 plane methods ---

    DECLARE DEF w1Fncx, w1Fncy, w1Wndx, w1Wndy   ! window/function transforms
    DECLARE DEF w1wWithin

    CALL w1Variables

    SUB w1Init
        BOX CLEAR worklft,w1Lft,w1Bas+3,w1Top-3
        CALL w1DrawPlane(1,1,1)                  ! grid, axes, zeroaxes
        CALL Grid1
        CALL SetTextFont(1,12,"bold")
        CALL PlotTextLJ(w1Rgt+8,w1y0+3,w1xAx$,axislabelclr)     ! axis labels
        CALL PlotTextCJ(w1x0,w1Top-10,w1yAx$,cyan)
        CALL w1KeepGridLayer
        CALL w1KeepGraphLayer
    END SUB

    SUB Grid1
        LOCAL i,wx
        SET COLOR drkmid
        FOR i= 2 to 6 step 2
            LET wx= w1Wndx(i*pi)
            PLOT wx,w1Top+1; wx,w1Bas-1
        NEXT i
    END SUB

    ! --- zoom buttons ---

    LET zmHgt = 17
    LET zmStp = zmHgt+2
    LET zmLft = w1Lft
    LET zmRgt = zmLft + 40
    LET zmTop = w1Bas + 30
    LET zmBas = zmTop + 3*zmStp + zmHgt

    SUB Zoom
        SELECT CASE zmBtn
        CASE 0
             LET w1fTop = 10
             LET w1ySTik=  1                     ! vertical axis Tik marks
             LET w1yLTik=  5
        CASE 1
             LET w1fTop = 1
             LET w1ySTik= 0.1                    ! vertical axis Tik marks
             LET w1yLTik= 0.5
        CASE 2
             LET w1fTop = 0.10001                ! needed offset numerics error
             LET w1ySTik= 0.01                   ! vertical axis Tik marks
             LET w1yLTik= 0.05
        CASE 3
             LET w1fTop = 0.010
             LET w1ySTik= 0.001                  ! vertical axis Tik marks
             LET w1yLTik= 0.005
        END SELECT
        LET w1fLft  =  0                         ! function bounds * pi
        LET w1fRgt  =  8
        LET w1fBas  = -w1fTop
        LET w1yLabel= w1yLTik
        LET w1yFirst= w1fBas

        CALL w1Variables
        CALL w1Init
    END SUB

    SUB ZoomInit
        CALL SetTextFont(1,12,"bold")
        FOR i = 0 to 3
            LET t= zmTop + i*zmStp
            LET b= t + zmHgt
            SELECT CASE i
            CASE 0
                 LET txt$= "10"
            CASE 1
                 LET txt$= "1"
            CASE 2
                 LET txt$= "0.1"
            CASE 3
                 LET txt$= "0.01"
            END SELECT
            CALL DrawButton(zmLft,zmRgt,b,t,5,txt$)
        NEXT i
    END SUB

    ! ---------- w2 initial values ------------
    ! --- w2 plane data ---

    DECLARE PUBLIC w2Lft,w2Rgt,w2Bas,w2Top,w2Midx,w2Midy
    DECLARE PUBLIC w2fLft,w2fRgt,w2fBas,w2fTop,w2x0,w2y0
    DECLARE PUBLIC w2xFirst, w2xSTik, w2xLTik, w2xLabel, w2xGridstep
    DECLARE PUBLIC w2yFirst, w2ySTik, w2yLTik, w2yLabel, w2yGridstep
    DECLARE PUBLIC w2wWid,w2wHgt,w2fWid,w2fHgt
    DECLARE PUBLIC w2fxRatio,w2fyRatio,w2wxRatio,w2wyRatio,w2Aspect
    DECLARE PUBLIC w2xPiFlag, w2xMult, w2yPiFlag, w2yMult

    LET w2Flag   = 1
    LET w2xPiFlag= 0
    LET w2xMult  = 1
    LET w2yPiFlag= 0
    LET w2yMult  = 1

    LET w2Lft = w1Lft                            ! window bounds
    LET w2Rgt = w1Lft + 100
    LET w2Top = workBas-142
    LET w2Bas = w2Top + 100

    LET w2fSize=  2
    LET w2fLft = -w2fSize                        ! function bounds
    LET w2fRgt =  w2fSize
    LET w2fTop =  w2fSize
    LET w2fBas = -w2fSize

    LET w2xAx$ = "x(0)"                          ! axis labels
    LET w2yAx$ = "x(0)"

    LET w2xGridstep= 1                           ! horizontal grid intervals
    LET w2yGridstep= 1                           ! vertical grid intervals

    LET w2xSTik = 0.5                            ! horizontal axis Tik marks
    LET w2xLTik = 1
    LET w2xLabel= 0
    LET w2xFirst= w2fLft

    LET w2ySTik = 0.5                            ! vertical axis Tik marks
    LET w2yLTik = 1
    LET w2yLabel= 0
    LET w2yFirst= w2fBas

    ! --- w2 Plane methods ---

    DECLARE DEF w2Fncx,w2Fncy,w2Wndx,w2Wndy      ! window/function transforms
    DECLARE DEF w2wWithin

    CALL w2Variables

    SUB w2Init
        CALL w2DrawPlane(1,1,1)                  ! grid, axes, zeroaxes
        CALL SetTextFont(1,12,"bold")
        CALL PlotTextLJ(w2Rgt+8,w2y0+3,w2xAx$,axislabelclr)     ! axis labels
        CALL StringWidth("x(0)",sw)
        LET lft= w2x0 - sw/2
        CALL PlotTextLJ(lft,w2Top-10,w2yAx$,axislabelclr)
        CALL PlotTextLJ(lft+2,w2Top-20,".",axislabelclr)
        CALL w2KeepGridLayer
    END SUB


    ! --- w3 plane data ---

    DECLARE PUBLIC w3Lft,w3Rgt,w3Bas,w3Top,w3Midx,w3Midy
    DECLARE PUBLIC w3fLft,w3fRgt,w3fBas,w3fTop,w3x0,w3y0
    DECLARE PUBLIC w3xFirst, w3xSTik, w3xLTik, w3xLabel, w3xGridstep
    DECLARE PUBLIC w3yFirst, w3ySTik, w3yLTik, w3yLabel, w3yGridstep
    DECLARE PUBLIC w3wWid,w3wHgt,w3fWid,w3fHgt
    DECLARE PUBLIC w3fxRatio,w3fyRatio,w3wxRatio,w3wyRatio,w3Aspect
    DECLARE PUBLIC w3xPiFlag, w3xMult, w3yPiFlag, w3yMult

    LET w3Flag   = 1
    LET w3xPiFlag= 0
    LET w3yPiFlag= 0
    LET w3xMult  = 1
    LET w3yMult  = 1

    LET w3Lft  = w2Rgt + 105                     ! pixel bounds
    LET w3Rgt  = w3Lft + 200
    LET w3Top  = workbas - 242
    LET w3Bas  = w3Top + 200

    LET w3fSize=  2
    LET w3fLft = -4                              ! function bounds
    LET w3fRgt =  0
    LET w3fTop =  w3fSize
    LET w3fBas = -w3fSize

    LET w3xAx$ = "Re"                            ! axis labels
    LET w3yAx$ = "Im"

    LET w3xGridstep= 1                           ! horizontal grid intervals
    LET w3yGridstep= 1                           ! vertical grid intervals

    LET w3xSTik = 0.5                            ! horizontal axis Tik marks
    LET w3xLTik = 1
    LET w3xLabel= 1
    LET w3xFirst= w3fLft

    LET w3ySTik = 0.5                            ! vertical axis Tik marks
    LET w3yLTik = 1
    LET w3yLabel= 1
    LET w3yFirst= w3fBas

    ! --- w3 Plane methods ---

    DECLARE DEF w3Fncx,w3Fncy,w3Wndx,w3Wndy      ! window/function transforms
    DECLARE DEF w3wWithin

    CALL w3Variables

    SUB w3Init
        CALL w3DrawPlane(1,1,1)                  ! grid, axes, zeroaxes
        CALL SetTextFont(1,12,"bold")
        CALL PlotTextLJ(w3Rgt+8,w3y0+3,w3xAx$,axislabelclr)     ! axis labels
        CALL PlotTextCJ(w3x0,w3Top-10,w3yAx$,axislabelclr)
        SET COLOR drkmid
        FOR ang= pi/2 to 3*pi/2 step pi/200
            LET x = cos(ang)
            LET y = sin(ang)
            LET wx= w3Wndx(x)
            LET wy= w3Wndy(y)
            PLOT wx,wy;
        NEXT ang
        PLOT
        CALL w3KeepGridLayer
    END SUB


    ! ---------- Slider parameters and methods ----------
    ! ---------------- vertical sliders -----------------

    LET slideHeight= 96

    ! --- vertical slider 1 ---

    DECLARE DEF v1Fncy,v1Wndy,v1Within           ! window/function transforms

    DECLARE PUBLIC v1axis,v1wLft,v1wRgt,v1wBas,v1wTop,v1sBas,v1sTop
    DECLARE PUBLIC v1fBas,v1fTop,v1First,v1STik,v1LTik,v1Label
    DECLARE PUBLIC v1name$,v1Mult,v1form$,v1clr,v1PiAxis

    LET v1PiAxis= 0
    LET v1Mult  = 1

    LET v1clr   = slideclr
    LET v1name$ = ""
    LET v1form$ = "-%.##"
    LET v1Places= 2
    LET v1Click = 0.5

    LET v1axis  = w2Lft - 24
    LET v1wBas  = w2Bas
    LET v1wTop  = w2Top
    LET v1fBas  = w2fBas
    LET v1fTop  = w2fTop

    LET v1STik  = 0.5
    LET v1LTik  = 1
    LET v1Label = 1
    LET v1First = v1fBas

    CALL v1SliderVariables

    SUB v1Init
        CALL v1DrawSlider(v1name$,y0)
    END SUB

    ! ----------- horizontal sliders ------------

    ! --- h1 slider - x0 ---

    DECLARE PUBLIC h1axis,h1wLft,h1wRgt,h1wBas,h1wTop,h1fLft,h1fRgt
    DECLARE PUBLIC h1name$,h1form$,h1clr,h1First,h1STik,h1LTik,h1Label
    DECLARE PUBLIC h1PiAxis,h1Mult,h1fMin,h1fMax

    DECLARE DEF h1Within

    LET h1PiAxis= 0
    LET h1Mult  = 1

    LET h1clr   = slideclr
    LET h1name$ = ""
    LET h1form$ = "-%.##"
    LET h1Places= 2
    LET h1Click = 0.5

    LET h1axis = w2Bas + 22
    LET h1wLft = w2Lft
    LET h1wRgt = w2Rgt

    LET h1fLft = w2fLft
    LET h1fRgt = w2fRgt

    LET h1STik = 0.5                             ! short tick marks
    LET h1LTik = 1                               ! long tick marks
    LET h1Label= 1                               ! labels
    LET h1First= h1fLft                          ! first tick mark

    CALL h1SliderVariables

    SUB h1Init
        CALL h1DrawSlider(h1name$,x0)
    END SUB

    ! --- h2 Slider - zeta ---

    DECLARE PUBLIC h2axis,h2wLft,h2wRgt,h2wBas,h2wTop,h2fLft,h2fRgt
    DECLARE PUBLIC h2name$,h2form$,h2clr,h2First,h2STik,h2LTik,h2Label
    DECLARE PUBLIC h2PiAxis,h2Mult,h2fMin,h2fMax

    DECLARE DEF h2Within

    LET h2PiAxis= 0
    LET h2Mult  = 1

    LET h2clr   = green
    LET h2name$ = "-Z"
    LET h2form$ = "-%.##"
    LET h2Places= 2
    LET h2Click = 0.25

    LET h2axis  = w3Bas + 22
    LET h2wLft  = w3Wndx(-1.25)
    LET h2wRgt  = w3Wndx( 0)

    LET h2fLft  = -1.25
    LET h2fRgt  =  0

    LET h2STik  =  0.25                          ! short tick marks
    LET h2LTik  =  1                             ! long tick marks
    LET h2Label =  0                             ! labels
    LET h2First = -1                             ! first tick mark

    CALL h2SliderVariables

    SUB h2Init
        CALL h2DrawSlider("",-z)
        CALL StringWidth(h2Name$,sw)
        CALL SwapZeta(h2wLft-7-sw,h2wBas-3,h2Name$,"Z",green)
    END SUB

    ! --- h3 slider ---

    DECLARE PUBLIC h3axis,h3wLft,h3wRgt,h3wBas,h3wTop,h3fLft,h3fRgt
    DECLARE PUBLIC h3name$,h3form$,h3clr,h3First,h3STik,h3LTik,h3Label
    DECLARE PUBLIC h3PiAxis,h3Mult,h3fMin,h3fMax

    DECLARE DEF h3Fncx,h3Within

    LET h3PiAxis= 0
    LET h3Mult  = 1

    LET h3clr   = litgry                         ! slideclr
    LET h3name$ = ""
    LET h3form$ = "-%.##"
    LET h3Places= 2
    LET h3Click = 0.1

    LET h3axis  = h2axis
    LET h3wLft  = w3Rgt + 115
    LET h3wRgt  = h3wLft + 100
    LET h3fLft  = 0
    LET h3fRgt  = 2

    LET h3STik  = 0.1
    LET h3LTik  = 0.5
    LET h3Label = 1
    LET h3First = h3fLft

    CALL h3SliderVariables

    SUB h3Init
        CALL h3DrawSlider("",w)
        CALL SuperSubScriptOmegaRJ(h3wLft-5,h3wBas-3,"w_[n]","w",litgry)
    END SUB


    ! ---------- Text Output Rects ----------

    ! ----- t1 DE -----

    ! x" + 2ZW_nx' + W_n^2x = 0

    LET t1BasLn= w1Top   - 13
    LET t1Lft  = w1Midx - 80
    LET t1Rgt  = h1wRgt  + 30
    LET t1Bas  = t1BasLn +  5
    LET t1Top  = t1BasLn - 15

    LET t1$= "w_[n]x' + w_[n]^[2]x = 0"          ! DE

    SUB t1Label
        LET lft= t1Lft
        CALL XDot2(lft,t1BasLn,cyan)

        CALL SwapZeta(lft,t1BasLn," + 2Z","Z",cyan)
        CALL StringWidth(" + 2Z",sw)
        LET lft= lft + sw + 2

        CALL SuperSubScriptOmegaLJ(lft,t1BasLn,"w_[n]","w",cyan)
        CALL StringWidth("wn",sw)
        LET lft= lft + sw

        CALL XDot1(lft,t1BasLn,cyan)

        CALL PlotTextLJ(lft,t1BasLn," + ",cyan)
        CALL StringWidth(" + ",sw)
        LET lft= lft + sw

        CALL OmegaSubNSqr(lft,t1BasLn,clr)

        CALL SetTextFont(1,12,"bold")
        CALL PlotTextLJ(lft,t1BasLn,"x = 0",cyan)
    END SUB

    SUB t1Clear
        BOX CLEAR t1Lft-2,t1Rgt,t1Bas,t1Top
    END SUB

    SUB t1Init
        CALL t1Label
    END SUB

    SUB XDot1(lft,bas,clr)
        CALL PlotTextLJ(lft,bas,"x",clr)
        CALL PlotTextLJ(lft+2,bas-9,".",clr)
        CALL StringWidth("x",sw)
        LET lft= lft + sw
    END SUB

    SUB XDot2(lft,bas,clr)
        CALL PlotTextLJ(lft,bas,"x",clr)
        CALL PlotTextLJ(lft,bas-9,".",clr)
        CALL PlotTextLJ(lft+4,bas-9,".",clr)
        CALL StringWidth("x",sw)
        LET lft= lft + sw
    END SUB

    SUB OmegaSubNSqr(lft,bas,clr)
        CALL SuperSubScriptOmegaLJ(lft,bas,"w_[n]","w",cyan)
        CALL StringWidth("w",sw)
        LET lft= lft + sw + 1
        CALL SetTextFont(1,9,"bold")
        CALL PlotTextLJ(lft,bas-6,"2",cyan)
        CALL StringWidth("2",sw)
        CALL SetTextFont(1,9,"bold")
        LET lft= lft + sw + 1
    END SUB

    ! --- t2  characteristic equation ---

    ! s^2 + 2ZW_ns + W_n^2 = 0

    LET t2BasLn= w3Midy + 3
    LET t2Lft  = h3wLft - 25
    LET t2Rgt  = workrgt
    LET t2Bas  = t2BasLn +  5
    LET t2Top  = t2BasLn - 15

    ! LET t2$ = "w_[n]s + w_[n]^[2] = 0"           ! characteristic equation

    SUB t2Label
        LET lft= t2Lft
        CALL SuperSubScriptLJ(lft,t2BasLn,"s^[2] + 2",cyan)
        CALL StringWidth("s2 + 2",sw)
        LET lft= lft + sw

        CALL SwapZeta(lft,t2BasLn,"Z","Z",cyan)
        CALL StringWidth("Z",sw)
        LET lft= lft + sw + 2

        CALL SuperSubScriptOmegaLJ(lft,t2BasLn,"w_[n]s + ","w",cyan)
        CALL StringWidth("wns + ",sw)
        LET lft= lft + sw

        CALL OmegaSubNSqr(lft,t2BasLn,cyan)

        CALL SetTextFont(1,12,"bold")
        CALL PlotTextLJ(lft,t2BasLn," = 0",cyan)
    END SUB

    SUB t2Clear
        BOX CLEAR t2Lft-2,t2Rgt,t2Bas,t2Top
    END SUB

    SUB t2Init
        CALL t2Label
    END SUB


    ! --- t3 text rectangle - root values ---

    LET t3BasLn1= t2BasLn + 35
    LET t3BasLn2= t3BasLn1 + 20
    LET t3Lft   = t2Lft
    LET t3Rgt   = workrgt
    LET t3Bas   = t3BasLn2 +  5
    LET t3Top   = t3BasLn1 - 15

    LET t3Label1$= "r_[1] = "
    LET t3Label2$= "r_[2] = "
    CALL StringWidth("r2 = ",sw)
    LET t3Eqx= t3Lft + sw

    SUB t3Label
        CALL SuperSubScriptRJ(t3Eqx,t3BasLn1,t3Label1$,yellow)
        CALL SuperSubScriptRJ(t3Eqx,t3BasLn2,t3Label2$,yellow)
    END SUB

    SUB t3SetRoots
        LOCAL r$,i$,z$
        CALL t3Clear

        IF abs(z)<1 then
           CALL Roots(real,imag,im1,im2)

           LET si1 = sgn(im1)
           LET s1$ = " + "
           LET si2 = sgn(im2)
           LET s2$ = " - "

           LET r$  = using$("-%.##",real*w)
           LET i1$ = using$("%.##",abs(im1*w))
           LET i2$ = using$("%.##",abs(im2*w))

           LET txt1$ = r$ & s1$ & i1$ & " i"
           LET txt2$ = r$ & s2$ & i2$ & " i"
           CALL PlotTextLJ(t3Eqx,t3BasLn1,txt1$,yellow)
           CALL PlotTextLJ(t3Eqx,t3BasLn2,txt2$,yellow)
        ELSE
           CALL RealRoots(r1,r2)
           LET r1$ = using$("-%.##",r1*w)
           LET r2$ = using$("-%.##",r2*w)

           LET txt1$ = r1$
           LET txt2$ = r2$
           CALL PlotTextLJ(t3Eqx,t3BasLn1,txt1$,yellow)
           CALL PlotTextLJ(t3Eqx,t3BasLn2,txt2$,yellow)
        END IF
    END SUB

    SUB t3Clear
        BOX CLEAR t3Eqx-2,t3Rgt,t3Bas,t3Top
    END SUB

    SUB t3Init
        CALL t3Label
        CALL t3SetRoots
    END SUB

    ! --- t4 text rectangle - rollover t,x values ---

    LET t4BasLn1= w3Top + 8
    LET t4BasLn2= t4BasLn1 + 20
    LET t4Lft   = t2Lft
    LET t4Rgt   = t4Lft + 100
    LET t4Bas   = t4BasLn2 +  5
    LET t4Top   = t4BasLn1 - 15
    LET t4Clr   = litgry

    LET t4Label1$= "t = "
    LET t4Label2$= "x = "
    CALL StringWidth(t4Label2$,sw)
    LET t4Eqx= t4Lft + sw

    SUB t4Label
        CALL SuperSubScriptRJ(t4Eqx,t4BasLn1,t4Label1$,t4Clr)
        CALL SuperSubScriptRJ(t4Eqx,t4BasLn2,t4Label2$,cyan)
    END SUB

    SUB t4SetCoords
        LET t = w1Fncx(mx)
        LET x = w1Fncy(my)
        LET t$= trim$(using$("--%.##",t))
        LET x$= trim$(using$("--%.##",x))
        CALL t4Clear
        CALL PlotTextLJ(t4Eqx,t4BasLn1,t$,t4Clr)
        CALL PlotTextLJ(t4Eqx,t4BasLn2,x$,cyan)
    END SUB

    SUB t4Clear
        BOX CLEAR t4Eqx-2,t4Rgt,t4Bas,t4Top
    END SUB

    SUB t4Init
        CALL t4Label
    END SUB


    ! --- default parameters ---

    LET w,oldw  = 1                              ! natural frequency & root modulus
    LET z,oldz  = 0.2                            ! damping ratio
    LET x0,oldx0= 1                              ! initial values
    LET v0,oldv0= 0

    LET zmBtn= 1

    ! --- Draw the screen ---

    CALL InitScreen

    SUB InitScreen
        BOX CLEAR worklft,workrgt,workbas,worktop

        CALL w1Init
        CALL w2Init
        CALL w3Init

        CALL v1Init
        CALL h1Init
        CALL h2Init


        CALL h3Init

        CALL t1Init
        CALL t2Init
        CALL t3Init
        CALL t4Init
        CALL ZoomInit

        CALL w1Wave
        CALL w2PlotInitialValues
        CALL w3DrawRoots
    END SUB


    ! ----------------- Event manager -----------------

    DO
       LET w1Clear= 0
       DO
          GET MOUSE: mx,my,ms
          IF w1wWithin(mx,my)=true then
             IF oldmx<>mx or oldmy<>my then
                CALL w1RollOver
             END IF
          ELSE IF w1Clear=1 then
             CALL w1RollOverClear
          END IF
       LOOP until ms=2                           ! mouse down?

       IF w1wWithin(mx,my)=true then
          DO
             GET MOUSE: mx,my,ms
             IF w1wWithin(mx,my)=true then
                IF oldmx<>mx or oldmy<>my then
                   CALL w1RollOver
                END IF
             ELSE IF w1Clear=1 then
                CALL w1RollOverClear
             END IF
          LOOP until ms=3
          IF w1Clear=1 then CALL w1RollOverClear

       ELSE IF w2wWithin(mx,my)=true then
          CALL w2MouseDrag(mx,my)

       ELSE IF v1Within(mx,my)=true then         ! x0
          IF mx<v1axis then
             CALL v1MouseClick(mx,my)
          ELSE
             CALL v1MouseDrag(mx,my)
          END IF

       ELSE IF h1Within(mx,my)=true then         ! x0
          IF my<h1axis then
             CALL h1MouseClick(mx,my)
          ELSE
             CALL h1MouseDrag(mx,my)
          END IF
       ELSE IF h2Within(mx,my)=true then         ! z
          IF my<h2axis then
             CALL h2MouseClick(mx,my)
          ELSE
             CALL h2MouseDrag(mx,my)
          END IF
       ELSE IF h3Within(mx,my)=true then         ! w
          IF my<h3axis then
             CALL h3MouseClick(mx,my)
          ELSE
             CALL h3MouseDrag(mx,my)
          END IF

       ELSE IF mx>=zmLft and mx<=zmRgt and my>=zmTop and my<=zmBas then
          LET zmBtn= int((my-zmTop)/zmStp)
          LET t = zmTop + zmBtn*zmStp
          LET b = t + zmHgt
          CALL MouseButtonUp(zmLft,zmRgt,b,t,ms)
          CALL Zoom
          CALL w1Wave

       ELSE IF infoWithin(mx,my,ms)=true then
          CALL infoButtonUp(ms)
          CALL InfoPage(Info$)
          CALL InitScreen
       ELSE IF quitWithin(mx,my,ms)=true then
          CALL quitButtonUp(ms)
          EXIT SUB
       ELSE
          CALL MouseUp(mx,my,ms)
       END IF
    LOOP

    ! --- Mouse Event Methods ---

    SUB w1RollOver                               ! cross hairs and cursor values
        CALL w1ShowGraphLayer
        SET COLOR litmid
        PLOT mx,w1Top+1; mx,w1Bas-1
        SET COLOR cyan
        PLOT w1Lft+1,my; w1Rgt-1,my
        CALL t4SetCoords

        LET w1Clear= 1
        CALL CopyCoords(mx,my,oldmx,oldmy)
    END SUB

    SUB w1RollOverClear
        CALL w1ShowGraphLayer
        LET w1Clear= 0
        CALL t4Clear
    END SUB

    ! --- initial value events ---

    SUB ResetInitialValues
        CALL w1Wave
        CALL w2PlotInitialValues
    END SUB

    ! --- w2 - v0 and x0 ---

    SUB w2MouseDrag(mx,my)
        DO
           CALL w2GetDragValues(mx,my,ms,2,2,x0,v0)
           IF x0<>oldx0 or v0<>oldv0 then
              CALL ResetInitialValues
              CALL h1Mark(x0)
              CALL v1Mark(v0)
              CALL CopyCoords(x0,v0,oldx0,oldv0)
           END IF
        LOOP until ms=3
    END SUB

    ! --- v1 - v0 ---

    SUB v1MouseClick(mx,my)
        LET oldv0= 999
        CALL v1GetClickVal(ms,v1Click,v0)
        CALL v1Action
    END SUB
    SUB v1MouseDrag(mx,my)
        DO
           CALL v1GetDragVal(ms,v1Places,v0)
           CALL v1Action
        LOOP until ms=3
    END SUB
    SUB v1Action
        IF v0<>oldv0 then
           CALL ResetInitialValues
           LET  oldv0= v0
        END IF
    END SUB

    ! --- h1 - x0 ---

    SUB h1MouseClick(mx,my)
        LET oldx0= 999
        CALL h1GetClickVal(ms,h1Click,x0)
        CALL h1Action
    END SUB
    SUB h1MouseDrag(mx,my)
        DO
           CALL h1GetDragVal(ms,h1Places,x0)
           CALL h1Action
        LOOP until ms=3
    END SUB
    SUB h1Action
        IF x0<>oldx0 then
           CALL ResetInitialValues
           LET  oldx0= x0
        END IF
    END SUB

    ! --- end of initial value events ---


    ! --- root events ---

    SUB ResetRootValues
        CALL w1Wave
        CALL t3SetRoots
        CALL w3DrawRoots
    END SUB

    ! --- h2 zeta ---

    SUB h2MouseClick(mx,my)
        CALL h2GetClickVal(ms,h2Click,z0)
        CALL h2Action
    END SUB
    SUB h2MouseDrag(mx,my)
        DO
           CALL h2GetDragVal(ms,h2Places,z0)
           CALL h2Action
        LOOP until ms=3
    END SUB
    SUB h2Action
        LET z= -z0
        IF z<>oldz then
           IF w=0 then
              CALL t3SetRoots
              CALL w3DrawRoots
           ELSE
              CALL ResetRootValues
           END IF
           LET  oldz= z
        END IF
    END SUB

    ! --- h3 w0 ---

    SUB h3MouseClick(mx,my)
        CALL h3GetClickVal(ms,h3Click,w)
        CALL h3Action
    END SUB
    SUB h3MouseDrag(mx,my)
        DO
           CALL h3GetDragVal(ms,h3Places,w)
           CALL h3Action
        LOOP until ms=3
    END SUB
    SUB h3Action
        IF w<>oldw then
           CALL ResetRootValues
           LET  oldw= w
        END IF
    END SUB

    ! --- end of root events ---


    ! ------ Graph drawing methods ------

    SUB w1Wave
        CALL SetConstants
        CALL w1ShowGridLayer

        LET az= abs(z)
        IF az=1 then                             ! critical
           LET y= fc(0)
        ELSE IF az<1 then                        ! under
           LET y= fu(0)
        ELSE                                     ! over
           LET y= fo(0)
        END IF
        CALL CopyCoords(w1Lft,w1Wndy(y),oldwx,oldwy)

        SET COLOR waveclr
        FOR wx= w1Lft to w1Rgt step 2
            LET x = w1Fncx(wx)
            IF az=1 then
               LET y= fc(x)
            ELSE IF az<1 then
               LET y= fu(x)
            ELSE
               LET y= fo(x)
            END IF
            LET wy= w1Wndy(y)

            IF wy>w1Top and wy<w1Bas and oldwy>w1Top and oldwy<w1Bas then      ! both in plane
               PLOT wx,wy; oldwx,oldwy
            ELSE IF (wy>w1Top and wy<w1Bas) or (oldwy>w1Top and oldwy<w1Bas) then   ! one in - clip
               CALL CopyCoords(oldwx,oldwy,wx1,wy1)
               CALL CopyCoords(wx,wy,wx2,wy2)
               CALL ClipVert(w1Bas,w1Top,wx1,wy1,wx2,wy2)
               PLOT wx1,wy1; wx2,wy2
            ELSE IF (wy>w1Bas and oldwy<w1Top) or (wy<w1Bas and oldwy>w1Top) then   ! one above and one below
               IF wy>oldwy then
                  PLOT oldwx,w1top+1; wx,w1bas-1
               ELSE
                  PLOT wx,w1top+1; oldwx,w1bas-1
               END IF
            END IF
            CALL CopyCoords(wx,wy,oldwx,oldwy)
        NEXT wx
        CALL w1KeepGraphLayer
    END SUB

    SUB w2PlotInitialValues
        CALL w2ShowGridLayer
        CALL w2MathToPixels(x0,v0,wx,wy)
        CALL PlotDiamondClr(wx,wy,white)
    END SUB

    SUB w3DrawRoots
        CALL w3ShowGridLayer
        LET az= abs(z)
        IF az<1 then                             ! complex roots
           CALL Roots(real,imag,im1,im2)

           LET wr = w3Wndx(-z)                   ! complex points
           LET wi1= w3Wndy(im1)
           LET wi2= w3Wndy(im2)
           SET COLOR litmid                      ! modulus
           PLOT wr,wi1; wr,wi2

           LET wr = w3Wndx(-z)                   ! complex points
           LET wi1= w3Wndy(im1)
           LET wi2= w3Wndy(im2)
           SET COLOR litmid                      ! modulus
           PLOT w3x0,w3y0; wr,wi1
           PLOT w3x0,w3y0; wr,wi2
           PLOT wr,wi1; wr,wi2

           LET wr = w3Wndx(w*real)               ! scaled complex points
           LET wi1= w3Wndy(w*im1)
           LET wi2= w3Wndy(w*im2)
           SET COLOR litmid                      ! modulus
           PLOT w3x0,w3y0; wr,wi1
           PLOT w3x0,w3y0; wr,wi2

           LET wr = w3Wndx(-z)                   ! complex points
           CALL PlotDiamondClr(wr,w3y0,green)

           LET wr = w3Wndx(w*real)               ! complex points
           LET wi1= w3Wndy(w*im1)
           LET wi2= w3Wndy(w*im2)
           CALL PlotDiamondClr(wr,wi1,rootclr)
           CALL PlotDiamondClr(wr,wi2,rootclr)
        ELSE                                     ! real roots
           CALL RealRoots(r1,r2)
           LET wz = w3Wndx(-z)                   ! -z value
           IF az=1 then                          ! one real root
              CALL PlotDiamondClr(wz,w3y0,green)
              LET wr= w3Wndx(r1*w)
              CALL PlotDiamondClr(wr,w3y0,rootclr)
           ELSE
              CALL PlotDiamondClr(wz,w3y0,green)

              LET wr1 = w3Wndx(r1*w)
              LET wr2 = w3Wndx(r2*w)
              CALL PlotDiamondClr(wr1,w3y0,rootclr)
              CALL PlotDiamondClr(wr2,w3y0,rootclr)
           END IF
        END IF
    END SUB
END SUB

! --- end of damping ratio code -------------