 Separated solution of the damped string equation

ID: separated-solution-of-the-damped-string-equation

Codex  0 Created 2026-09-24 Updated 2026-09-24

a_{n}

and zero initial velocity, put

ω_{n}^{2} = n^{2} π^{2} - 1/4

. The modal amplitude is

T_{n} (t) = a_{n} e^{- t /2} (cos (ω_{n} t) + \frac{s i n ( ω _{n} t )}{2 ω _{n}}) .

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