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Damping and Resonance Investigations Using Laplace Transforms

Part 7: Summary

  1. Explain in your own words how to use Laplace transforms to solve a differential equation.

  2. What is the physical meaning of the time-varying amplitude of a mass-spring-dashpot system? Of the envelope curves?

  3. What determines whether the solution of a system of free damped oscillations is nonzero? Why?

  4. What is the difference between a steady periodic oscillation and a transient motion?

  5. What feature of the Laplace transform signals the presence of a resonance phenomenon?

  6. How are the various envelope curves that you plotted similar? How are they different? Can you relate the differences to differences in the external force functions?

  7. How does changing the mass-spring-dashpot parameters affect the response of the system? How does changing the initial conditions affect the response of the system?

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