A damped harmonic oscillator is given by [f(t)=left{begin{array}{cc} A e^{-alpha t} e^{i omega_{0} t}, & t geq 0 0, & t <0 end{array} ight.]

A damped harmonic oscillator is given by

\[f(t)=\left\{\begin{array}{cc} A e^{-\alpha t} e^{i \omega_{0} t}, & t \geq 0 \\ 0, & t<0 \end{array}\right.\]

a. Find \(\hat{f}(\omega)\) and

b. the frequency distribution \(|\hat{f}(\omega)|^{2}\).

c. Sketch the frequency distribution.