A test mass on a spring mount 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 test mass on a spring mount has ω0=10 rad s−1\omega_0 = 10\,\mathrm{rad\,s^{-1}} and γ=2.0 s−1\gamma = 2.0\,\mathrm{s^{-1}}. It sits at rest at equilibrium until, at t=0t=0, a shaker starts pushing it with F(t)/m=(1.0 m s−2)cos⁡ωtF(t)/m = (1.0\,\mathrm{m\,s^{-2}})\cos\omega t at ω=ω0\omega=\omega_0. ((a)) Find the steady response xp(t)x_{\mathrm{p}}(t) as a real function of time. ((b)) Find the displacement x(t)x(t) for t>0t>0. ((c)) The shaker's operator says the motion jumps straight to its steady amplitude. Show that it does not, and estimate how long the amplitude takes to reach 9090 per cent of its steady value.

Browse the problem library