A force has band limited white noise with frequency bounds of \(\omega_{1}=100 \mathrm{rad} / \mathrm{s}\) and \(\omega_{2}=500 \mathrm{rad} / \mathrm{s}\) and magnitude \(S_{0}=2 \times 10^{2} \mathrm{~N}^{2} \cdot \mathrm{s} / \mathrm{rad}\) determine the following.

(a) The autocorrelation function for the force

(b) The expected mean square value of the force

(c) Assuming the mean is zero, what is the probability that the magnitude of the force is greater than \(1000 \mathrm{~N}\) ?