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

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Physics

A spring-mass system has a spring constant of 3 N/m. A mass of 2kg is attached to the spring, and the motion takes place in aviscous fluid that offers a resis- tance numerically equal to themagnitude of the instanta- neous velocity. If the system is drivenby an external force of (12 cos 3t − 8 sin 3t) N, determine thesteady-state response.

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

  2. (b) Verify that the amplitude predicted by your work in (a) foran ex- ternal force f(t) = cos(3t) is consistent with the amplitudeof the response you found in the body of the problem (that they donot match exactly may be attributable to the phase shift in theforcing).

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