Problem 3: Consider the spring-mass system shown below. A mass of m = 5 kg has stretched a spring by so = 1.5 meters and is at rest. A damping system is connected that provides a damping force equal to 30 times the instantaneous velocity of the mass. At time t = 0, the mass at rest has an external force of f(t) = 25 sin(10+) applied. Unstretched y=0m k C m f(t) a) Write a differential equation that models the mass location (7)as a function of time. Solution: Put your math/explanation here..... b) Identify an appropriate solution technique, and solve the differential equation for y(I). Solution: Put your math/explanation here... c) Use MATLAB to plot your solution for /= 0 to /= 20. Solution: Scode d) What is the steady-state solution of y(t)? Solution: Put your math/explanation here.... e) Use the MATLAB dsolve() function to solve the differential equation and plot the solution on a new figure. The results provided by dsolve() and your solution from part (b) should match. Solution: Scode