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- Vui - where, wn is the (a) Show that the maximum oscillation amplitude occurs when natural frequency of the system. 2m (b) Show that the maximum oscillation amplitude at that frequency is A - where, wa is the frequency of the undriven, damped system.

- Vui - where, wn is the (a) Show that the maximum oscillation amplitude occurs when natural frequency of the system. 2m (b) Show that the maximum oscillation amplitude at that frequency is A - where, wa is the frequency of the undriven, damped system.

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a damped mass-spring sytem with mass m, spring constant k and damping constant b is driven by an eternal force with frequency w and amplitute Fo

(a) Show that the maximum oscillation amplitude occurs when w - where, wn is the natural frequency of the system. 4 Fo (b) Show that the maximum oscillation amplitude at that frequency is A – frequency of the undriven, damped system. where, wa is the
Transcribed Image Text:(a) Show that the maximum oscillation amplitude occurs when w - where, wn is the natural frequency of the system. 4 Fo (b) Show that the maximum oscillation amplitude at that frequency is A – frequency of the undriven, damped system. where, wa is the
Expert Solution
Step 1

Given, for a damped motion m is the mass, k is the spring constant and b is the damping constant.

Also ωo is the frequency of external force with amplitude Fo.

And the equation of motion for a damped harmonic oscillator is,

md2xdt2+bdxdt+kx=Fmd2xdt2+bdxdt+kx=Fosinωot

Then the solution for this equation will be in the following form, 

x=Asinωt-θ

where A is the amplitude, θ is the phase difference. And the amplitude can be written as,

A=Fomωo2-ω22+4b2m2ω2

 

 

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