Poles
and Vibrations -- Help |
The graphing window shows a sum of two damped oscillations, x = A e^{at}cos(bt) + B e^{ct}cos(dt) = Re ( Ae^{zt} + Be^{wt }) where z = a + bi and w = c + di and A, a, b, B, c, and d are real. The complex number a + bi is shown as a green diamond, and the complex number c + di is shown as a red diamond, in the complex plane at lower right. Control the parameters A, a, b, B, c, and d using the sliders below, or (in the case of a, b, c, d) by dragging the appropriate diamond in the complex plane window. If
A = 0 the a, b sliders and the green diamond are turned off. Click
on the [Envelope] key to display an envelope, indicating the rate of
growth or decay of x(t). |