An undamped oscillator obeys x + 25x = 8 5t m ,s^ -2

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Oscillations, Waves & Acoustics · Simple, damped and driven oscillations

Mathematical Methods for Physics, Ch Higher-order linear equations, the Wronskian and variation of parameters

Problem

An undamped oscillator obeys

\ddot{x} + 25x = 8\cos 5t\ \mathrm{m\,s^{-2}}.

A first attempt guesses the trial particular integral

x_{\mathrm{p}} = A\cos 5t + B\sin 5t

with

A

and

B

constants to be found. ((a)) Decide whether this trial function can work, giving the reason. ((b)) If it cannot, state the corrected trial form that undetermined coefficients should use instead (do not evaluate its coefficients).

Related theory

Ordinary differential equations

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