Consider the periodic excitation below.

a$)$ Represent and plot the signal with $1,10,100$ non$-$zero fourier terms. $($Attach MATLAB code$).$

b$)$ Solve the differential equation: $($mx$($t$)..)+($cx$($t$).)+$kx$($t$)=$kf$($t$)$ by means of Fourier Analysis, where f$($t$)$ is the periodic function above.

c$)$ Plot the response of the system including $1,10$ and $100$ non$-$zero Fourier terms. Use m$=1$ kg$,$ c$=1$Ns$/$m$,$ k $=100$ N$/$m$,$ A $=1$ N and T $=1$ s$.($Attach MATLAB code$).$