A machine is given an impact force by an impact hammer. If the machine can be modelled as a single-degree-of-freedom system with m = 10 kg, k = 4000 N/m, and c = 40 N.s/m, and the magnitude of the impact is F = 100 N.S. (1) Determine the time response of the machine analytically. (ii) Plot the analytical response of the machine using any computational software of choice. (iii) Use the Runge-Kutta integration scheme to calculate and plot the response of the system. You should plot the numerical response over the analytical response. (iv) Plot the frequency response function (FRF) of the system making sure that your frequency range covers the resonant frequency.