A perfectly elastic string of equilibrium length 4 metres is released from rest in a trapezoidal configuration shown here
The string is clamped at both ends (x = 0 and
x = 4).
Waves move on the string with speed c.
There is no friction.
Determine the subsequent evolution of the displacement
y(x, t) of the string.
The governing partial differential equation is
The complete solution is a Fourier sine series in x:
The plot (for c = 1) is generated from the first six
non-trivial terms in the Fourier series.
As one can see, the convergence is fairly good.
The Maple file is available here.
[Return to your previous page]
[Return to the home page for this course]
-
Created 2010 07 15 and most recently modified 2010 07 15 by
Dr. G.H. George