Question $1$

Consider a damped SDOF system as shown in Figure Qla. Assume that m$=5$ kg$,$ c$=300N.\frac{s}{m},k=8000\frac{N}{m},$ and $y(t)$ is indicated in Figure Q$1$b$.$ Find the steady$-$state response of this system by using:

a$)$ Fourier transform method $($by considering n from $0$ tol $10$ in Fourier series$)$

b$)$ Runge$-$Kutta method in the interval $0\mathrm{.}0.$

Plot the response which $is$ determined from these two methods for the interval $0.$