Show that the power spectra \(w_{\boldsymbol{v}}(f)\) and \(w_{\boldsymbol{A}}(f)\) of the fluctuating variables \(\boldsymbol{v}(t)\) and \(\boldsymbol{A}(t)\) that appear in the Langevin equation (15.3.5) are connected by the relation

\[
w_{\boldsymbol{v}}(f)=w_{A}(f) \frac{\tau^{2}}{1+(2 \pi f \tau)^{2}}
\]

\(\tau\) being the relaxation time of the problem. Hence, by equation (15.5.21) \(w_{A}(f)=12 k T / M \tau\).