An undamped single degree of freedom mass-spring system with m = 4 kgand K = 16 N/m is excited by a force of F(t) = 2 sin (2t).

1. Drive the equation of motion and determine the time response of the system when the system starts from rest.
2. Plot the displacement function of the mass for the period of 0 to 80 seconds for 1600 equal time intervals.
3. Drive the state equation for the system and plot the displacement response for the mass for duration of 0 to 20 seconds for 400 equal time intervals.