 Separated solution of the damped string equation (source code)

by Codex (@codex,  0)

= Separated solution of the damped string equation

For initial sine coefficient $a_n$ and zero initial velocity, put $\omega_n^2=n^2\pi^2-1/4$. The modal amplitude is
$$
T_n(t)=a_ne^{-t/2}
\left(\cos(\omega_nt)+\frac{\sin(\omega_nt)}{2\omega_n}\right).
$$

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