Setup¶
Plot motion of a string with fixed ends, with given normal mode coefficients¶
Example 1¶
For initial condition $y(x,t=0) = a x (L-x)$, where $a$ is a constant with the correct units, we get $c_n = a \frac{4-4\cos(k_n L) - 2k_n L \sin(k_n L)}{k_n^3 L}$.
Example 2: Problem 4.3¶
For the initial condition of problem 3 in problem sheet 4, we get $c_n = \frac{32 d}{3 n^2 \pi^2} \sin(n\pi/4)$. In the plot, we use $d=1$.
Example 3: Problem 5.1¶
The solution for problem 5.1 is $c_n = \frac{2 i v_1}{v k_n^2 L} \left(\cos(k_n x_2) - \cos(k_n x_1)\right)$