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.
