# Damped Harmonic Oscillator

(A) A damped oscillator is described by the equation:

m [(x)ddot] = ?b [(x)dot] ? kx

What is the condition for critical damping? Assume this condition is satisfied.

(B) For t < 0 the mass is at rest at x = 0. The mass is set in motion by a sharp impulsive force at t = 0, so that the velocity is v0 at time t = 0. Determine the position x(t) for t > 0.

(C) Determine the maximum displacement of the mass for t > 0.

(D) Suppose m = 1 kg and squareroot{k/m} = 2(pi)rad/s. Calculate the maximum displacement for t > 0, as a function of v0. Hand in an accurate graph of xmax versus v0.

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#### Solution Summary

We solve problems involving a damped harmonic oscillator.

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