Question

A simple damped mechanical harmonic oscillator with damping constant γ is driven by a force ?0?????....

A simple damped mechanical harmonic oscillator with damping constant γ is driven by a force ?0?????. Show that the FWHM of the amplitude A(ω) vs. angular frequency ω curve is ?√3. You can assume that Q>>1 and ω is very close to ω0. Formulae in the book can be used. But you will have to reference the page and equation number.

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Answer #1

The differential equation of a forced damped harmonic oscillation:

The solution is/;

The amplitude A and phase d as a function of the driving frequency are

and

The maximum amplitude Amax occurs at the driving frequency   given by

Assuming that  that Q>>1 and ω is very close to ω0.

Tha graph shows a plot . Note that FWHM =

to plot i have taken

FWHM = 2 x = 3.5

if it helps kindly upvote.

comment below for doubts

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