A mass-spring oscillator has a mass of 2 kg, a spring constant of 34 N/m and a damping constant of 4 Ns/m. It is stretched to a displacement of 10 m and released from rest. a. Assuming there are no external forces, model the spring's displacement as a function of time. Graph your answer and describe its asymptotic behavior in a sentence. b. Now assume that at t seconds, there is an external force (in Newtons) given by Fexr(t) = 130 cos(t). (Assume the external force is oriented parallel to the spring) Write an initial value problem describing the motion of the system. c. Solve the above system to write the displacement as a function of time. Graph your answer and describe its asymptotic behavior in a sentence. d. Repeat parts b and c, assuming there is no friction.
