It is desired to approximate the random displacement of a machine due to a random force \(F(t)\). What are the SI units of the following.

(a) The power spectral density of the displacement \(S_{x}(\omega)\)

(b) The power spectral density of the force \(S_{F}(\omega)\)

(c) The Fourier transform of the force \(F(\omega)\)

(d) The Fourier transform of the displacement \(X(\omega)\)

(e) The transfer function for the system \(H(\omega)\)

(f) The mean square value of the displacement \(E\left(x^{2}\right)\)

(g) The variance of the force \(\sigma_{F}^{2}\)

(h) The autocorrelation function for the displacement \(R_{x}(\tau)\)

(i) The autocorrelation function for the force \(R_{F}(\tau)\)

(j) The probability distribution for the force

(k) The probability density function for the force