For the unexcited (no external force applied) system of Figure P2.16, do the following:

a. Write the differential equation that describes the system.

b. Assuming initial conditions x(0) = x_{0} and ẋ(0) = x_{1}, write a Laplace transform expression for X(s).

c. Find x(t) by obtaining the inverse Laplace transform from the result in Part c.