12. A spring-mass system has: m=4kg, k=64 N/m. The initial conditions are as follows: x=-0.5m x'=0m/s . An external force F = 8sin (41) is acting on the mass. Construct a differential equation characterizing the response of the mass and solve it. Plot the response to 10 sec and confirm that this is a resonance phenomenon. Look at your solution again; can you see why you have the resonance? - cos 4t sin 4ticos 41 - 2 16 4