The graphing window displays graphs of solutions, with rest initial conditions, of the equation

\[\ddot{x} + 2\zeta\omega_n \dot{x} + \omega_n 2x = f(t)\]

for several standard input signals \(f(t)\):

the delta function, the unit step function, and the unit ramp function (\(f(t) = t\) for \(t \lt 0\), \(f(t) = 0\) for \(t \lt 0\)).

Graphs of the input function itself is also displayed in a paler color. Sliders control the system parameters \(\zeta\) and \(\omega_n\). Toggles specify display of the delta response (cyan), the step response (green), and the ramp response (yellow). A slider at bottom right controls the vertical scale.

The roots of the characteristic polynomial are displayed at lower left.

A cursor roll-over brings up cross-hairs and a readout of the \(t\) and \(x\) coordinates.

© 2008 H. Miller and J.-M. Claus