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Damping and Resonance Investigations Using Laplace Transforms

Part 4: An Exponentially Damped Periodic Force

  1. This time, the periodic external force is exponentially damped, namely

    f(t) = 900 e-t/5 cos(3t).

    Note that the transform Y(s) includes a repeated quadratic factor that signals the presence of a resonance phenomenon. Plot the oscillations and the envelope curves.

  2. Where are the oscillations of the mass increasing in amplitude? Where are they decreasing?

  3. What is the maximum value of the amplitude function? Where does it occur?

  4. What happens to the oscillations as t goes to infinity?

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