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 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.