Introduction to Classical Mechanics · Problem 4.30

Conservation of energy and momentum — Morin

Physics — Mechanics · driven-harmonic-motion

Problem

A particle of mass

m

is subject to a spring force,

-kx

, and also a driving force,

F_d \cos\omega_d t

. But there is no damping force. Find the particular solution for

x(t)

by guessing

x(t) = A\cos\omega_d t + B\sin\omega_d t

. If you write this in the form

C\cos(\omega_d t - \phi)

, where

C > 0

, what are

C

and

\phi

? Be careful about the phase (there are two cases to consider).