Vibrations and Waves · Problem 3-13

Forced vibrations and resonance — A.P. French

Physics — Waves · damped-oscillator-solution-verification

Problem

Verify that

x = Ae^{-\alpha t} \cos \omega t

is a possible solution of the equation

\frac{d^2x}{dt^2} + \gamma \frac{dx}{dt} + \omega_0^2 x = 0

and find

\alpha

and

\omega

in terms of

\gamma

and

\omega_0