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Consider a vibrating system described by the initial value problem y?? + 0.25y? + 2y = 2 cos?t, y(0) = 0, y? (0) = 2. (a

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Consider a vibrating system described by the initial value problem y?? + 0.25y? + 2y = 2 cos?t, y(0) = 0, y? (0) = 2. (a) Determine the steady-state part of the solution of this problem. (b) Find the gain function ?G(i?)? of the system. (c) Plot ?G(i?)? and ?(?) = ?arg(G(i?)) versus ?. (d) Find the maximum value of ?G(i?)? and the frequency ? for which it occurs.

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