A window at right displays the graph of a solution to the differential equation mx" + bx' + kx = 0 .
Positions on the graph are set using a time slider under the window or [<], [>], keys. The [>>] key starts an animation. Rolling the cursor over this window creates crosshairs and a readout of the values of t and x.

The initial conditions are set by a mouse click on the window at left, or using the x' and x sliders. It is indicated by a yellow diamond connected by a line segment to the origin. When the value of t is changed the value of x(t) and x'(t) are recorded in this window as well, and the curve traced by (x', x) is faintly drawn. The [Relate diagrams] key toggles a faint yellow line connecting the point on the (x', x) plane with the corresponding point on the graph.

Sliders at lower left control values of m, b, and k.

The [Roots] key toggles a display of the roots of the characteristic polynomial p(s) = ms² + bs + k , and their values are read out at lower right, in green if non-real, blue if real and distinct, and red if repeated.

© 2008 H. Hohn, H. Miller and J.-M. Claus