Question

Damped motion in excercises 11-14, consider a damped mass-spring system whose motion is described by the differential equation.

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The zeros of its characteristic equation are:

 

and

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For the system is overdamped; , it is critically damped; and for it is underdamped.

a) Determine wheter the differential equation represents an overdamped, critically damped, or underdamped system.

b) Find the particular solution that satisfies the initial conditions.

c) Use a graphing utility to graphe the particular solution found in part (b). Explain how the graph illustrates the type of damping in the system.

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