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A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is...

A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is attached to the spring, and the motion takes place in a viscous fluid that offers a resistance numerically equal to the magnitude of the instantaneous velocity.

(a) If the system is driven by an external force of (12 cos 3t − 8 sin 3t) N, determine the steady-state response.

(b) Find the gain function if the external force is f(t) = cos(ωt).

(c) Verify that the amplitude predicted by your work in (a) for an ex- ternal force f(t) = cos(3t) is consistent with the amplitude of the response you found in the body of the problem (that they do not match exactly may be attributable to the phase shift in the forcing).

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