The graphing window at the top displays a solution to the differential equation x" + 2ζω_nx' + ω_n²x = 0.

Adjust initial conditions by dragging the cursor over the bottom left graphing window, in which x(0) is recorded on the vertical axis and x'(0) is recorded on the horizontal axis. Alternatively, set these values using the sliders along the bottom and left side of the initial condition window.

Adjust the values of the natural circular frequency ω_n and the damping ratio ζ using sliders at bottom right.

The damping ratio slider actually displays -ζ. The graphing window above that slider displays the complex number -ζ in green, and, in yellow, the two roots of the characteristic polynomial. These roots are also read out to the right.

The trajectory of (x',x) is drawn in light gray in the upper left window, and the position of (x',x) on that curve is indicated by a yellow diamond and strut from the origin. Selecting [Relate diagrams] illustrates the
equality of the x cooridinate of the point in phase space with the value of the solution.!elect the vertical scale for the graphing window using the buttons below it.

Roll over the graphing window to display crosshairs and a readout of the coordinates.

© 2001 H. Hohn