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 conjugate pair a ± bi is shown as green diamonds, and
the complex conjugate pair c ± di is shown as red diamonds, 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.
©
2001 H. Hohn