# Spring Oscillations

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A particle of mass ,m, is at rest at the end of a spring(force constant=k)hanging from a fixed support. At t=0 a constant downward forcd F is applied to the mass and acts for a time T. Show that after the force is removed, the displacement of the mass from its equilibrium position (x=Xe, where x is down) is:

x - Xe =F/k[cosW(t-T) - cosw(t)]

where w = omega

Â© BrainMass Inc. brainmass.com December 15, 2022, 5:37 pm ad1c9bdddfhttps://brainmass.com/physics/equilibrium/spring-oscillations-94485

#### Solution Summary

This solution shows that after the force is removed, the displacement of mass from equilibrium position is x - Xe =F/k[cosW(t-T) - cosw(t)]. Steps are shown for the full derivations for where the concepts of Hooke's Law and period are used.

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