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The motion of an harmonic oscillator is governed by the differential equation 2¨x + 3 ˙x...

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Physics

The motion of an harmonic oscillator is governed by thedifferential equation 2¨x + 3 ˙x + 4x = g(t).

i. Suppose the oscillator is unforced and the motion is startedfrom rest with an initial displacement of 5 positive units from theequilibrium position. Will the oscillator pass through theequilibrium position multiple times? Justify your answer.

ii. Now suppose the oscillator experiences a forcing function 2et for the first two seconds, after which it is removed. Later, theoscillator is given a blow with a hammer that instantaneouslyimparts 3 units of force at precisely 5 seconds. Find g(t) in thiscase. No points awarded for answers written piecewise.

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