!  x" + bx' + kx = 0
!  s^2 + bs + k = 0
! -b +-sqrt(b^2 - 4k) / 2
!  discriminant = b^2 - 4k
!  b = sqrt(4k) then there is one real root and critical damping
!  b > sqrt(4k) then the roots are real and it is overdamped
!  b < sqrt(4k) then the roots are complex and it is underdamped

!  Damped Vibes: Rather than just a rollover vertical line, let's have crosshairs,
!  parallel with Damping Constant. Also in parallel, let's switch to scale buttons
!  .01, .1, 1, 10, and eliminate the "maximum x" text. 

!  Damped Vibrations
!  
!  Set the initial conditions on the window at left or using the sliders.
!  
!  Set the spring constant  k  and the damping constant  b  using the sliders 
!  at lower left. 
!  
!  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.

!  Critical Damping is the least amount of damping required to
!  return a system to its equilibrium state without oscillation.


! 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

! x'' + B/m sqrt(k/m) x' + k/m x = 0
! w_n = sqrt(k/m)
! B/m sqrt(k/m) = 0


!! File: DampedVibrations.68k
!! June 6, 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= 800
LET window$= "The d'Arbeloff Interactive Math Project"
LET colorscheme= 0

LET title$ = "Damped Vibrations"

SUB ThisProgram
    CALL InitialConditions
    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$= "click the mouse or press a key to close..."
CALL PlotTextCJ(workmidx,(workbas+worktop)/2,quit$,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.trc"
!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 ------
! -----------------------------------------------------------


! ***

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

    DECLARE DEF quitWithin,infoWithin

    ! --- help screen array ---

    DIM  info$(1:8)
    MAT READ info$

    DATA "Damped Vibrations"
    DATA ""
    !    DATA "The differential equation is x'' + bx' + kx = 0"
    !    DATA "The characteristic equation is s^[2] + bs + k = 0"
    !    DATA "The roots of the characteristic equation are"
    !
    !    DATA "-r1 = -b + sqrt(b^[2]-4k) / 2"
    !    DATA "-r2 = -b - sqrt(b^[2]-4k) / 2"
    !    DATA "and the discriminant = b^[2] - 4k."
    !    DATA ""
    !    DATA "If b^[2] - 4k = 0, then b = sqrt(4k), and this is called critical damping, or b_[c]. Critical damping is the least amount of damping required to return a system to its equilibrium state without oscillation."
    !
    !    DATA "The ratio b/b_[c] is called the damping ratio. If the damping coefficient b is equal to the critical damping b_[c] the damping ratio is 1."
    !    DATA "If b > b_[c] the damping ratio is greater than 1 and the vibration is overdamped."
    !    DATA "If b < b_[c] the damping ratio is less than 1 and the vibration is underdamped."
    !    DATA ""

    DATA "Set the initial conditions by clicking or dragging the mouse on the left plane,"
    DATA "or by clicking or dragging the x(0) and x'(0) sliders."

    DATA "Set the spring constant  k  and the damping constant  b  using the sliders at lower left."
    DATA "Clicking a slider among the tik marks gives values rounded to the nearest tenth."
    DATA ""
    DATA "Click the number buttons to reset the vertical scale of the time series plane."
    DATA ""
    DATA "Roll the cursor over the time series plane to display crosshairs and the values of  t  and  x."

    !  Damped Vibrations
    !  
    !  Set the initial conditions on the window at left or using the sliders.
    !  
    !  Set the spring constant  k  and the damping constant  b  using the sliders 
    !  at lower left. 
    !  
    !  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.

    !  Critical Damping is the least amount of damping required to
    !  return a system to its equilibrium state without oscillation.

    ! --- color definition and adjustment ---

    LET pdclr = green
    LET ivclr = yellow
    LET fldclr= drkmid
    LET posclr= yellow
    LET velclr= litgry                           !cyan
    LET trclr = blue
    LET dmpclr= red

    SET COLOR MIX(blue) .4,.6,1

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

    DECLARE DEF clamp,roundn,e

    ! ---- Functions ----

    LET dt= 1/64
    DEF dxdt(p,v)=  v
    DEF dvdt(p,v)= -b*v - k*p + cos(omega*t)

    ! I have three signals in mind
    ! 0 ,  cos(omega t) ,  and  sq(omega t)

    ! There are two basic solutions to the "homogeneous equation"
    !   x" + bx' + kx = 0
    !   y(t)  with  y(0) = 1  and  y'(0) = 0
    !   z(t)  with  z(0) = 0  and  z'(0) = 1

    SUB SetW(b,k, w)
        LET w= sqr(abs((b/2)^2 - k))
    END SUB

    SUB SetCritDamp(k,critDamp)
        LET critDamp = 2 * sqr(k)
        LET critDamp = sqr(4*k)
        IF k>0 then
           LET dampRatio= round(b/critDamp,4)
        END IF
    END SUB

    SUB SetNatFreq(k,natFreq)
        LET natFreq= sqr(k)
    END SUB

    SUB SetD(b,k,omega, D)
        LET D= (k-omega^2)^2 + omega^2*b^2
    END SUB

    SUB SetRS(b,w, r,s)
        LET r= -b/2 + w
        LET s= -b/2 - w
    END SUB

    SUB SetVars
        CALL SetW(b,k, w)
        ! CALL SetD(b,k,omega, D)
        CALL SetRS(b,w, r,s)
        CALL SetCritDamp(k, critDamp)
        LET b2= b*b
        LET k4= k*4
    END SUB

    SUB InitialVals(b,k,omega,D, fxp0,dxp0)
        LET fxp0=  (k-omega^2)/D
        LET dxp0= -(omega^2*b)/D
    END SUB

    SUB InitialDifs
        LET deltax= pos-fxp0
        LET deltad= vel-dxp0
    END SUB

    DEF y(t)                                     ! velocity ?
        ! print b,critDamp
        IF b>critDamp then
           LET y= 1/(s-r) * (s*e^(r*t) - r*e^(s*t))
        ELSE IF b<critDamp then
           LET y= e^(-b*t/2)*(cos(w*t) + (b/(2*w))*sin(w*t))
        ELSE
           LET y= (1 + b*t/2) * e^(-b*t/2)
        END IF
    END DEF

    DEF z(t)                                     ! acceleration ?
        IF b>critDamp then
           LET z= -1/(s-r) * (e^(r*t) - e^(s*t))
        ELSE IF b<critDamp then
           LET z= 1/w * e^(-b*t/2) * sin(w*t)
        ELSE
           LET z= t * e^(-b*t/2)
        END IF
    END DEF


    DEF xp(t)                                    ! periodic solution for f(t)= cos(wt)
        LET xp= 1/D * ( (k-omega^2)*cos(omega*t) - (omega*b)*sin(omega*t) )
    END DEF

    DEF tr(t)                                    ! transient
        LET tr= deltax*y(t) + deltad*z(t)
    END DEF

    DEF fx(t)                                    ! solution
        ! LET fx= tr(t) + xp(t)
        LET fx = pos*y(t) + vel*z(t)
    END DEF


    ! Case:  f(t) = 0 (There's no frequency omega in this case). 
    ! If the initial condition on the phase plane reads (x(0),x'(0)),
    ! then the graph plots:
    !   x(t) = x(0)*y(t) + x'(0)*z(t)


    ! Case:  f(t) = cos(omega t)
    ! Then the periodic solution is given by

    !   D = (k-omega^2)^2 + omega^2*b^2
    !   xp(t) = 1/D * ( (k-omega^2)*cos(omega*t) - (omega*b)*sin(omega*t) )

    ! The initial value is

    !   xp(0)  = (k - omega^2)/D
    !   xp'(0) = -(omega^2*b)/D

    ! and so when this menu choice is opened xp(t) should be drawn 
    ! and this cursor point appears on the phase plane. 
    !
    ! When the user moves to the point (x(0),x'(0)) on the phase plane,
    ! the solution becomes  

    !   x(t) = xp(t) + (x(0)-xp(0))*y(t) + (x'(0)-xp'(0))*z(t)


    SUB RungeKutta4(x,v)
        LET dx1= dxdt(x,v)
        LET dv1= dvdt(x,v)
        LET x1 = x + .5*dx1*dt
        LET v1 = v + .5*dv1*dt
        LET dx2= dxdt(x1,v1)
        LET dv2= dvdt(x1,v1)
        LET x2 = x + .5*dx2*dt
        LET v2 = v + .5*dv2*dt
        LET dx3= dxdt(x2,v2)
        LET dv3= dvdt(x2,v2)
        LET x3 = x + dx3*dt
        LET v3 = v + dv3*dt
        LET dx4= dxdt(x3,v3)
        LET dv4= dvdt(x3,v3)

        LET dv = (dv1 + 2*dv2 + 2*dv3 + dv4) / 6
        LET dx = (dx1 + 2*dx2 + 2*dx3 + dx4) / 6
        LET v  = v + dt*dv
        LET x  = x + dt*dx
    END SUB

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

    LET wsize = 160
    LET fsize =   4
    LET whgt  = 200
    LET fhgt  =   1

    ! --- 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 = workRgt - 430                    ! pixel bounds
    LET w1Rgt = w1Lft + 400                      ! 360
    LET w1Top = workTop + 65
    LET w1Bas = w1Top + whgt

    LET w1fLft=  0                               ! function bounds
    LET w1fRgt=  4
    LET w1fTop=  fhgt
    LET w1fBas= -fhgt

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

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

    LET w1xSTik = 1                              ! horizontal axis Tik marks
    LET w1xLTik = 2
    LET w1xLabel= 2
    LET w1xFirst= w1fLft

    LET w1ySTik = 1                              ! vertical axis Tik marks
    LET w1yLTik = 2
    LET w1yLabel= 2
    LET w1yFirst= w1fBas


    ! --- w1 Plane methods ---

    DECLARE DEF w1Fncx,w1Fncy,w1Wndx,w1Wndy,w1Within  ! window/function transforms

    CALL w1Variables

    SUB w1Init
        BOX CLEAR w1Lft-40,w1Lft-4,w1Bas+8,w1Top-8
        CALL w1Reset(zoomstate)
        CALL w1DrawPlane(1,1,1)                  ! x axis, y axis, zeroaxes

        CALL SetTextFont(1,12,"bold")
        CALL PlotTextLJ(w1Rgt+8,w1y0+3,w1xAx$,axislabelclr)     ! axis labels

        LET  ybas= w1Top-11
        CALL PlotTextCJ(w1x0,ybas,w1yAx$,yellow)

        CALL w1KeepGridLayer
    END SUB

    SUB w1Reset(zoomState)
        SELECT CASE zoomState
        CASE 0
             LET w1fTop = 2
             LET w1ySTik= 0.5                    ! vertical axis Tik marks
             LET w1yLTik= 1
        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  = 4
        LET w1fBas  = -w1fTop
        LET w1xSTik = 0.5                        ! horizontal axis Tik marks
        LET w1xLTik = 1
        LET w1xLabel= 1
        LET w1xFirst= w1fLft
        LET w1yLabel= w1yLTik
        LET w1yFirst= w1fBas

        CALL w1Variables
    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 ZoomInit
        CALL SetTextFont(1,12,"bold")
        FOR i= 0 to 3
            LET top= zmTop + i*zmStp
            LET bas= top + zmHgt
            SELECT CASE i
            CASE 0
                 LET txt$= "2"
            CASE 1
                 LET txt$= "1"
            CASE 2
                 LET txt$= "0.1"
            CASE 3
                 LET txt$= "0.01"
            END SELECT
            CALL DrawButton(zmLft,zmRgt,bas,top,5,txt$)
        NEXT i
    END SUB


    ! ------------------------------------------
    ! --- 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 = worklft+65                       ! pixel bounds
    LET w2Rgt = w2Lft+whgt
    LET w2Top = w1Top
    LET w2Bas = w2Top+whgt

    LET w2fLft= -fhgt                            ! function bounds
    LET w2fRgt=  fhgt
    LET w2fTop=  fhgt
    LET w2fBas= -fhgt

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

    LET w2xGridstep= 0                           ! grid line intervals
    LET w2yGridstep= 0

    LET w2xSTik = 0.1                            ! axis Tik marks
    LET w2xLTik = 0.5
    LET w2xLabel= 0.5
    LET w2xFirst= w2fLft

    LET w2ySTik = 0.1
    LET w2yLTik = 0.5
    LET w2yLabel= 0.5
    LET w2yFirst= w2fBas


    ! --- plane 2 methods ---

    DECLARE DEF w2Fncx,w2Fncy,w2Wndx,w2Wndy      ! window/function transforms
    DECLARE DEF w2wWithin,w2Within

    CALL w2Variables

    SUB w2Init
        CALL w2DrawPlane(0,0,1)                  ! x axes, y axes, zeroaxes
        CALL SetTextFont(1,12,"bold")

        CALL PlotTextLJ(w2Rgt+9,w2y0+3,w2xAx$,velClr)      ! axis labels
        CALL PlotTextCJ(w2Rgt+13,w2y0-7,".",velClr)

        CALL PlotTextCJ(w2x0,w2Top-11,w2yAx$,yellow)

        CALL w2KeepGridLayer
        CALL w2KeepGraphLayer
    END SUB


    ! ---------- Slider parameters and methods ----------

    ! ---------------- v1 vertical slider - initial position -------

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

    LET v1PiAxis= 0
    LET v1Mult  = 1

    LET v1Clr   = yellow
    LET v1name$ = ""
    LET v1form$ = "-%.##"
    LET v1Places= 2
    LET v1Click = 0.1

    LET v1axis  = w2Lft - 25
    LET v1wBas  = w2Bas
    LET v1wTop  = w2Top
    LET v1fBas  = w2fBas
    LET v1fTop  = w2fTop

    LET v1STik  =  0.1
    LET v1LTik  =  0.5
    LET v1Label =  0.5
    LET v1First = -1

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

    CALL v1SliderVariables

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

    ! --- horizontal sliders ---

    LET slideWidth= 200

    ! --- h1 Slider - initial velocity ---

    DECLARE PUBLIC h1axis,h1wLft,h1wRgt,h1wBas,h1wTop,h1fLft,h1fRgt
    DECLARE PUBLIC h1name$,h1form$,h1clr,h1First,h1STik,h1LTik,h1Label
    DECLARE PUBLIC h1PiAxis,h1Mult,h1Min,h1Max

    DECLARE DEF h1Within                         ! window/function transforms

    LET h1Flag  = 0
    LET h1PiAxis= 0
    LET h1Mult  = 1

    LET h1clr   = velClr
    LET h1name$ = ""
    LET h1form$ = "-%.##"
    LET h1Places= 2
    LET h1Click = 0.1

    LET h1axis  = w2Bas + 24
    LET h1wLft  = w2Lft
    LET h1wRgt  = h1wLft + slidewidth

    LET h1fLft  = w2fLft
    LET h1fRgt  = w2fRgt                         ! needs 4 if critical damping is on

    LET h1STik  = w2xSTik
    LET h1LTik  = w2xLTik
    LET h1Label = w2xLabel
    LET h1First = w2xFirst

    CALL h1SliderVariables

    DECLARE DEF h1Wndx

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

    ! --- h2 Slider - b damping ---

    DECLARE PUBLIC h2axis,h2wLft,h2wRgt,h2wBas,h2wTop,h2fLft,h2fRgt
    DECLARE PUBLIC h2name$,h2form$,h2clr,h2First,h2STik,h2LTik,h2Label
    DECLARE PUBLIC h2PiAxis,h2Mult,h2Min,h2Max

    DECLARE DEF h2Within                         ! window/function transforms

    LET h2Flag  = 0
    LET h2PiAxis= 0
    LET h2Mult  = 1

    LET h2clr   = slideclr
    LET h2name$ = "b"
    LET h2form$ = "-%.##"
    LET h2Places= 2
    LET h2Click = 0.1

    LET h2axis  = w2Bas + 150
    LET h2wLft  = w2Lft
    LET h2wRgt  = h2wLft+slidewidth

    LET h2fLft  = 0
    LET h2fRgt  = 4                              ! needs 4 if critical damping is on

    LET h2STik  = 0.1
    LET h2LTik  = 0.5
    LET h2Label = 1
    LET h2First = h2fLft

    CALL h2SliderVariables

    DECLARE DEF h2Wndx

    SUB h2Init
        CALL h2DrawSlider(h2name$,b)
    END SUB


    ! --- h3 slider - k - spring constant ---

    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 h3Within                         ! window/function transforms

    LET h3Flag  = 0
    LET h3PiAxis= 0
    LET h3Mult  = 1

    LET h3clr   = slideclr
    LET h3name$ = "k"
    LET h3form$ = "-%.##"
    LET h3Places= 2

    LET h3axis  = h2axis+65
    LET h3wLft  = h2wLft
    LET h3wRgt  = h3wLft+slideWidth

    LET h3fLft  = 0
    LET h3fRgt  = 4.0

    LET h3STik  = 0.1
    LET h3LTik  = 0.5
    LET h3Label = 1
    LET h3First = h3fLft
    LET h3Click = 0.1

    CALL h3SliderVariables

    SUB h3Init
        CALL h3DrawSlider(h3name$,k)
    END SUB

    ! --- Text Output Rects ----------
    ! --- text rectangle 1 ---

    LET t1BasLn= w1Top - 30
    LET t1txt$ = "x + bx + kx = 0"
    CALL SetTextFont(1,12,"bold")
    CALL StringWidth(t1txt$,sw)

    LET t1Lft  = w1Midx - sw/2
    LET t1Rgt  = t1Lft + sw + 20
    LET t1Bas  = t1BasLn +  5
    LET t1Top  = t1BasLn - 15

    LET t1Label$= ""

    SUB t1Label
        CALL SuperSubScriptRJ(t1Lft,t1BasLn,t1Label$,white)
    END SUB

    SUB t1Set
        CALL SetTextFont(1,12,"bold")
        LOCAL r$,i$,z$
        CALL t1Clear
        CALL PlotTextLJ(t1Lft,t1BasLn,t1txt$,yellow)

        LET dot2= t1Lft + 4
        CALL PlotTextCJ(dot2,t1BasLn-10,"..",yellow)

        CALL StringWidth("x + b",sw)
        LET dot1= t1Lft + sw + 4
        CALL PlotTextCJ(dot1,t1BasLn-10,".",yellow)
    END SUB

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

    SUB t1Init
        CALL t1Set
    END SUB


    ! --- text rectangle 2 ---

    LET t2BasLn1 = h2wBas - 3
    LET t2BasLn2 = t2BasLn1+20
    LET t2Lft    = w1Lft
    LET t2Rgt    = t2Lft + 99
    LET t2Top    = t2BasLn2 - 15
    LET t2Bas    = t2BasLn2 +  5
    LET t2Eq1$   = "sqrt(4k)"
    LET t2Label2$= " = "
    CALL SetTextFont(1,12,"bold")
    CALL StringWidth("bc = ",sw)
    LET t2eqx    = t2Lft+sw
    LET t2form$  = "-%.##"
    LET t2Clr    = litgry

    SUB t2Label
        CALL SetTextFont(1,12,"bold")
        CALL PlotTextRJ(t2eqx,t2BasLn1,t2Label2$,t2Clr)
        CALL StringWidth("bc = ",sw)
        CALL Setbc(t2Eqx-sw,t2BasLn1,t2Clr)
        !CALL PlotTextLJ(t2eqx,t2BasLn1,t2Eq1$,t2Clr)
        CALL RootSign(t2eqx,t2BasLn1,26,t2Clr)
        CALL PlotTextLJ(t2Eqx+8,t2BasLn1,"4k",t2Clr)
        CALL PlotTextRJ(t2eqx,t2BasLn2,t2Label2$,t2Clr)
    END SUB

    SUB t2Value
        CALL SetTextFont(1,12,"bold")
        CALL t2ClearVal
        CALL PlotTextLJ(t2Eqx,t2BasLn2,using$(t2form$,critDamp),t2Clr)
    END SUB

    SUB t2ClearVal
        BOX CLEAR t2eqx-6,t2Rgt,t2Bas,t2Top
    END SUB
    SUB t2Clear
        BOX CLEAR t2Lft-2,t2Rgt,t2Bas,t2Top
    END SUB

    SUB t2Init
        CALL t2Label
        CALL t2Value
    END SUB

    ! --- text rectangle 5 ---

    LET t5BasLn1 = t2BasLn1
    LET t5BasLn2 = t2BasLn2
    LET t5BasLn3 = t5BasLn2 + 20
    LET t5Lft    = w1Lft + 150
    LET t5Top    = t5BasLn2 - 15
    LET t5Bas    = t5BasLn2 +  5
    LET t5Label1$= "damping ratio = "
    LET t5Label2$= " = "
    CALL SetTextFont(1,12,"bold")
    CALL StringWidth(t5Label1$,sw)
    LET t5Eqx    = t5Lft + sw
    LET t5Rgt    = t5Eqx + 99
    LET t5form$  = "-%.##"
    LET t5Clr    = litgry

    SUB t5Label
        CALL SetTextFont(1,12,"bold")
        CALL PlotTextRJ(t5eqx,t5BasLn1,t5Label1$,t5Clr)
        CALL PlotTextLJ(t5Eqx,t5BasLn1,"b/",t5Clr)
        CALL StringWidth("b/",sw)
        CALL Setbc(t5Eqx+sw+1,t5BasLn1,litgry)
        CALL PlotTextRJ(t5eqx,t5BasLn2,t5Label2$,t5Clr)
    END SUB

    SUB t5Value
        CALL SetTextFont(1,12,"bold")
        CALL t5ClearVal
        IF k>0 then
           LET damp$= using$(t5form$,dampRatio)
        ELSE
           LET damp$= "infinite"
        END IF
        CALL PlotTextLJ(t5Eqx,t5BasLn2,damp$,t5Clr)

        IF dampRatio<1 then
           LET damp$= "underdamped"
        ELSE IF dampRatio>1 then
           LET damp$= "overdamped"
        ELSE
           LET damp$= "critically damped"
        END IF
        IF k=0 then LET damp$= ""

        IF damp$<>oldDamp$ then
           LET oldDamp$= damp$
           BOX CLEAR t5Lft-2,t5Rgt,t5BasLn3+5,t5BasLn3-15
           CALL PlotTextLJ(t5Lft,t5BasLn3,damp$,t5Clr)
        END IF
    END SUB

    SUB t5ClearVal
        BOX CLEAR t5eqx-6,t5Rgt,t5Bas,t5Top
    END SUB
    SUB t5Clear
        BOX CLEAR t5Lft-2,t5Rgt,t5Bas,t5Top
    END SUB

    SUB t5Init
        CALL t5Label
        CALL t5Value
    END SUB

    ! --- text rectangle 3 ---

    LET t3BasLn1 = w1Bas+62
    LET t3BasLn2 = t3BasLn1+20
    LET t3Lft    = w2Lft                         !+ 115
    LET t3Rgt    = t3Lft + 99
    LET t3Top    = t3BasLn1 - 15
    LET t3Bas    = t3BasLn2 +  5
    LET t3Label1$= "x(0) = "                     ! x
    LET t3Label2$= "x(0) = "                     ! x'
    CALL SetTextFont(1,12,"bold")
    CALL StringWidth(t3Label1$,sw)
    LET t3eqx    = t3Lft+sw
    LET t3form$  = "-%.##"

    CALL StringWidth(t3form$,sw)
    LET t3tRgt= t3eqx + sw

    SUB t3Label
        CALL SetTextFont(1,12,"bold")
        CALL PlotTextRJ(t3eqx,t3BasLn2,t3Label1$,posclr)
        CALL PlotTextRJ(t3eqx,t3BasLn1,t3Label2$,velclr)
        CALL PlotTextCJ(t3Lft+4,t3BasLn1-10,".",velclr)
    END SUB

    SUB t3Set
        CALL SetTextFont(1,12,"bold")
        CALL t3ClearVal
        CALL PlotTextRJ(t3tRgt,t3BasLn2,using$(t3form$,pos),posclr)
        CALL PlotTextRJ(t3tRgt,t3BasLn1,using$(t3form$,vel),velclr)
    END SUB

    SUB t3Clear
        BOX CLEAR t3Lft-2,t3Rgt,t3Bas,t3Top
    END SUB
    SUB t3ClearVal
        BOX CLEAR t3eqx-6,t3Rgt,t3Bas,t3Top
    END SUB

    SUB t3Init
        CALL t3Label
        CALL t3Set
    END SUB

    ! ------ t4 text output - initial values -------

    CALL SetTextFont(1,12,"bold")
    LET t4BasLn1 = w1Bas+62
    LET t4BasLn2 = t4BasLn1+20
    CALL StringWidth("x = 55.55555",sw)
    LET t4Lft    = w1Rgt-sw
    LET t4Rgt    = w1Rgt
    LET t4Bas    = t4BasLn2 +  5
    LET t4Top    = t4BasLn1 - 15
    LET t4clr1   = litgry
    LET t4clr2   = yellow
    LET t4Label1$= "t = "
    LET t4Label2$= "x = "
    CALL StringWidth(t4Label2$,sw)
    LET t4Eqx    = t4Lft + sw

    SUB t4Init
        CALL t4Clear
        CALL PlotTextRJ(t4Eqx,t4BasLn1,t4Label1$,t4clr1)
        CALL PlotTextRJ(t4Eqx,t4BasLn2,t4Label2$,t4clr2)
        CALL t4Values
    END SUB

    SUB t4Clear
        BOX CLEAR t4Lft-2,t4Rgt+2,t4Bas,t4Top
    END SUB

    SUB t4ClearValues
        BOX CLEAR t4Eqx-2,t4Rgt+2,t4Bas,t4Top
    END SUB

    SUB t4Values
        CALL t4ClearValues
        LET n1$= using$("--%.#####",t)
        LET n2$= using$("-%.#####",x)
        CALL PlotTextRJ(t4Rgt,t4BasLn1,n1$,t4clr1)
        CALL PlotTextRJ(t4Rgt,t4BasLn2,n2$,t4clr2)
    END SUB


    ! --- radio buttons ---

    DECLARE PUBLIC r1cnt,r1stp,r1siz
    DECLARE PUBLIC r1lft,r1rgt,r1bas,r1top,r1Name$,r1NameClr
    DECLARE PUBLIC r1NameList$(),r1ColorList()

    MAT redim r1NameList$(1:3)
    MAT READ r1NameList$
    DATA "0.02","2","4"

    MAT redim r1ColorList(1:3)
    MAT READ r1ColorList
    DATA 21,21,21

    LET r1cnt    = 3
    LET r1Lft    = w1Lft
    LET r1Top    = w1Bas+47
    LET r1Name$  = "maximum x"
    LET r1NameClr= 21

    DECLARE DEF r1Within

    CALL r1SetVars


    ! --- default parameters ---

    LET b,oldb    = 1.0
    LET k,oldk    = 1.0
    LET vel,olddx0= 0
    LET pos,oldfx0= 0.5

    LET zoomstate = 1

    LET critMarks = 0
    CALL SetVars

    ! --- Draw the screen ---

    CALL InitScreen

    SUB InitScreen
        BOX CLEAR worklft,workrgt,workbas,worktop

        CALL w1Init
        CALL w2Init

        CALL v1Init
        CALL h1Init
        CALL h2Init
        CALL h3Init

        IF critMarks=1 then CALL MarkCritDamp(k)
        CALL t1Init
        IF critMarks=1 then CALL t2Init
        IF critMarks=1 then CALL t5Init
        CALL t3Init

        CALL zoomInit
        CALL w2Point(vel,pos)
        CALL w1PlaneGraphs
    END SUB


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

    DO
       IF ms<>2 then
          LET clearFlag= 0
          BOX KEEP w1Lft,w1Rgt,w1Bas,w1Top in temp$
          DO
             GET MOUSE: mx,my,ms
             IF w1Within(mx,my)=true then
                CALL w1RollOver
             ELSE IF clearFlag=1 then
                CALL w1RollOverClear
             END IF
          LOOP until ms=2
       END IF
       IF clearFlag=1 then
          CALL w1RollOverClear
       END IF

       IF w2Within(mx,my)=true then
          CALL w2MouseClickOrDrag

          ! sliders

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

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

       ELSE IF mx>zmLft and mx<zmRgt and my>zmTop and my<zmBas then
          LET zoomstate= int((my-zmTop)/zmStp)
          LET top= zmTop + zoomstate*zmStp
          LET bas= top+zmHgt
          CALL MouseButtonUp(zmLft,zmRgt,bas,top,ms)

          CALL w1Reset(zoomstate)
          CALL w1Init
          CALL w1PlaneGraphs

       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
        CALL w1wClamp(mx,my)
        IF mx<>oldmx or my<>oldmy then
           BOX SHOW temp$ at w1Lft,w1Bas
           CALL PlotLine(mx,w1Top+1, mx,w1Bas-1, litmid)
           CALL PlotLine(w1Lft+1,my, w1Rgt-1,my, litmid)
           LET t= w1Fncx(mx)
           LET x= fx(t)
           CALL t4Init
           CALL CopyCoords(mx,my,oldmx,oldmy)
           LET clearFlag= 1
        END IF
    END SUB

    SUB w1RollOverClear
        CALL t4Clear
        BOX SHOW temp$ at w1Lft,w1Bas
        LET clearFlag= 0
    END SUB

    SUB w2MouseClickOrDrag
        LET oldmx,oldmy= -999
        DO
           GET MOUSE: mx,my,ms
           CALL w2wClamp(mx,my)
           IF mx<>oldmx or my<>oldmy then
              CALL w2PixelsToMath(mx,my,vel,pos)
              CALL v1Mark(pos)
              CALL h1Mark(vel)
              CALL w2Point(vel,pos)
              CALL w1PlaneGraphs
              CALL CopyCoords(mx,my,oldmx,oldmy)
              LET olddx0= vel
              LET oldfx0= pos
           END IF
        LOOP until ms=3
    END SUB

    SUB w2Point(vel,pos)
        CALL w2ShowGridLayer
        CALL t3Set
        CALL w2MathToPixels(vel,pos,wx,wy)
        CALL PlotDiamondClr(wx,wy,yellow)
    END SUB

    ! ----- v1 slider event -----

    SUB v1MouseClick
        CALL v1GetClickVal(ms,v1Click,pos)
        CALL v1Action
    END SUB
    SUB v1MouseDrag
        DO
           CALL v1GetDragVal(ms,v1Places,pos)
           CALL v1Action
        LOOP until ms=3
    END SUB

    SUB v1Action
        IF pos<>oldfx0 then
           CALL v1Mark(pos)
           CALL w2Point(vel,pos)
           CALL w1PlaneGraphs
           LET oldfx0= pos
        END IF
    END SUB

    ! ----- h1 slider event -----

    SUB h1MouseClick
        CALL h1GetClickVal(ms,h1Click,vel)
        CALL h1Action
    END SUB
    SUB h1MouseDrag
        DO
           CALL h1GetDragVal(ms,h1Places,vel)
           CALL h1Action
        LOOP until ms=3
    END SUB

    SUB h1Action
        IF vel<>olddx0 then
           CALL h1Mark(vel)
           CALL w2Point(vel,pos)
           CALL w1PlaneGraphs
           LET olddx0= vel
        END IF
    END SUB

    ! ----- h2 slider event -----

    SUB h2MouseClick
        CALL h2GetClickVal(ms,h2Click,b)
        CALL H2Action
    END SUB
    SUB h2MouseDrag
        DO
           CALL h2GetDragVal(ms,h2Places,b)
           CALL h2Action
        LOOP until ms=3
    END SUB

    SUB h2Action
        IF b<>oldb then
           CALL w1PlaneGraphs
           IF critMarks=1 then CALL t5Value
           LET oldb= b
        END IF
    END SUB

    SUB MarkCritDamp(k)
        CALL SetCritDamp(k,critDamp)
        LET wcd  = h2Wndx(critDamp)
        LET cdTop= h2wBas+2
        CALL ValueMarker(h2wLft,h2wRgt,wcd,cdtop,litgry)
    END SUB

    SUB ValueMarker(wLft,wRgt,wx,wTop,clr)
        SET COLOR litgry
        LET wBas= wTop+6
        BOX CLEAR wLft-5,wRgt+15,wBas+15,wTop
        PLOT wx,wTop; wx,wBas
        PLOT wx,wTop; wx+2,wTop+2; wx-2,wTop+2; wx,wTop
        CALL Setbc(wx-4,wBas+11,litgry)
        !CALL SuperSubScriptLJ(wx-4,wBas+11,"b_[c]",litgry)
        CALL t2Value
    END SUB

    SUB Setbc(bclft,bcbas,bcclr)
        CALL SetTextFont(1,12,"bold")
        CALL PlotTextLJ(bclft,bcbas,"b",bcclr)
        CALL StringWidth("b",sw)
        CALL PlotTextLJ(bclft+sw,bcbas+4,"c",bcclr)
    END SUB

    ! ----- h3 slider event -----

    SUB h3MouseClick
        CALL h3GetClickVal(ms,h3Click,k)
        CALL h3Action
    END SUB
    SUB h3MouseDrag
        DO
           CALL h3GetDragVal(ms,h3Places,k)
           CALL h3Action
        LOOP until ms=3
    END SUB

    SUB h3Action
        IF k<>oldk then
           IF critMarks=1 then
              CALL MarkCritDamp(k)
              !  CALL MarkNatFreq(k)
              CALL t5Value
           END IF
           CALL w1PlaneGraphs
           LET oldk= k
        END IF
    END SUB

    ! --- Graphing routines ---

    SUB w1PlaneGraphs
        CALL SetVars
        CALL w1ShowGridLayer

        SET COLOR yellow
        LET oldwy= w1Wndy(fx(0))
        LET oldwx= w1Lft
        FOR wx= w1Lft to w1Rgt
            LET t = w1Fncx(wx)
            LET x = fx(t)
            LET wy= w1Wndy(x)

            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   ! above and 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
        PLOT
    END SUB
END SUB

! --- end of damped vibrations code -------------------