Problem $3.$ Using the modulation property determine $($and plot amplitude spectra$)$ the Fourier transform of the following signals

$x_1(t)=sinc(t)cos(2t)$

$x_2(t)=sinc(t)cos(2t)cos(4t)$

$x_3(t)=\{\begin{array}{ccc}4cos(100t),& \text{f}\text{o}\text{r}& -5t5\\ 0,& \text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}& \end{array}.$

This signal represents the switched sinusoid$,$ i$.$e$.,$ the sinusoid is switched on and off at the points $t=-5$ and $t=5,$ respectively.