Classical Dynamics of Particles and Systems · Problem 3-9

Nonlinear Oscillations and Chaos — Marion & Thornton

Physics — Mechanics · step-function-response

Problem

A particle of mass mm is at rest at the end of a spring (force constant =k= k) hanging from a fixed support. At t=0t = 0, a constant downward force FF is applied to the mass and acts for a time t0t_0. Show that, after the force is removed, the displacement of the mass from its equilibrium position (x=x0x = x_0, where xx is down) is x−x0=Fk[cos⁡ω0(t−t0)−cos⁡ω0t]x - x_0 = \frac{F}{k}[\cos\omega_0(t - t_0) - \cos\omega_0 t] where ω02=k/m\omega_0^2 = k/m.

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