Consider a mass-spring system governed by the second order differential equation of the form my" +ry' +ky = f(t). i) Suppose that you are considering free motion of the system (that is f(t)= 0). Assume that m = 1;r 10;k =16 and the initial conditions y(0) = 1 and y'(0) = 0. Find the motion of the system. Is the system underdamping or overdamping? Suppose, you want to design the system for critical damping, what value should you choose for k? ii) Suppose you are considering forced motion of the system with m 1;r 0; k = 16; f(t)= sin4t and y(0)= y'(0) = 0. Then what kind of solution do you expect. Discuss the solution. What will happen if you include the effects of damping force to this system?

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