A vibration-isolation mount for a pump is heavily damped on purpose: it has and

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Simple, damped and driven oscillations · Simple, damped and driven oscillations

Mathematical Methods for Physics, Ch Second-order linear equations: damping, driving and resonance

Problem

A vibration-isolation mount for a pump is heavily damped on purpose: it has ω0=120 rad s−1\omega_0 = 120\,\mathrm{rad\,s^{-1}} and γ=80 s−1\gamma = 80\,\mathrm{s^{-1}}, and the pump drives it with F0/m=36 m s−2F_0/m = 36\,\mathrm{m\,s^{-2}} at an angular frequency ω\omega that can be set anywhere. ((a)) Find the drive frequency ωmax⁡\omega_{\max} at which the steady amplitude is largest. ((b)) Find the largest steady amplitude, and compare it with the amplitude when the drive is at ω0\omega_0. ((c)) Find the two drive frequencies at which ∣A~∣2|\tilde{A}|^2 falls to half its largest value, compare their separation with γ\gamma, and say why the rule that the half-power full width is γ\gamma fails here.

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