A mass of 2 kg is attached to the end of a spring whose restoring force is 160 N

Question

A mass of 2 kg is attached to the end of a spring whose restoring force is 160 N/m. The mass is in a medium that exerts a viscous resistance of 132 N when the mass has a velocity of 6 m/s. The viscous resistance is proportional to the speed of the object.

Suppose the spring is stretched 0.03 m beyond the its natural position and released. Let positive displacements indicate a stretched spring, and suppose that external vibrations act on the mass with a force of 2 sin(3 t) N at time t seconds.

Find an function to express the steady-state component of the object's displacement from the spring's natural position, in m after t seconds. (Note: This spring-mass system is not "hanging", so there is no gravitational force included in the model.)

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Explanation / Answer

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