Show that the convolution integral, Eq. (4.31), can also be expressed in terms of the response to a unit step function \(h(t)\) as

\[x(t)=F(0) h(t)+\int_{0}^{t} \frac{d F(\tau)}{d \tau} h(t-\tau) d \tau\]

Equation 4.31:-

F(T)e (-) sin wd (t - T) dr (4.31) x(t) == mwd F(T