Classical Mechanics (Kibble & Berkshire) · Problem 5.12

Energy conservation — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · driven-linear-oscillations-fourier-series

Problem

Solution by Fourier series A driven oscillator satisfies the equation

\ddot{x} + 2K\dot{x} + \Omega^2 x = F(t),

where

K

and

\Omega

are positive constants. Find the driven response of the oscillator to the 'saw tooth' input, that is, when

F(t)

is given by

F(t) = F_0 t \qquad (-\pi < t < \pi)

and

F(t)

is periodic with period

2\pi

. [It is a good idea to sketch the graph of the function

F(t)