Vibrations and Waves · Problem 4-13

Coupled oscillators and normal modes — A.P. French

Physics — Waves · power-resonance-curve

Problem

The graph shows the power resonance curve of a certain mechanical system when driven by a force

F_0 \sin \omega t

, where

F_0 =

constant and

\omega

is variable. (a) Find the numerical values of

\omega_0

and

Q

for this system. (b) The driving force is turned off. After how many cycles of free oscillation is the energy of the system down to

1/e^5

of its initial value? (

e = 2.718

.) (To a good approximation, the period of free oscillation can be set equal to

2\pi/\omega_0