A SDOF system with a mass of (20 mathrm{~kg}, zeta=0.1), and (omega_{n}=100 mathrm{rad} / mathrm{s}) is subject

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A SDOF system with a mass of \(20 \mathrm{~kg}, \zeta=0.1\), and \(\omega_{n}=100 \mathrm{rad} / \mathrm{s}\) is subject to white noise with \(S_{0}=1 \times 10^{-2} \mathrm{~N}^{2} \cdot \mathrm{s} / \mathrm{rad}\).

(a) What is the mean square value of the response of the system?

(b) What is the probability of the response exceeding \(5 \mathrm{~mm}\) ?

(c) What is the probability of the maximum of the response exceeding \(5 \mathrm{~mm}\) ?

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