Poles and Vibrations -- Help


The graphing window shows a sum of two damped oscillations,

x = A eatcos(bt) + B ectcos(dt) = Re ( Aezt + Bewt )

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.
If B = 0 the c, d sliders and the red diamond are turned off.

Click on the [Envelope] key to display an envelope, indicating the rate of growth or decay of x(t).
This is ±Aeat if a > c or B = 0, ±Bect if c > a or A = 0.