Problem 28. Consider the following differential equation for a spring-mass system with a piecewise forcing term:
x''(0) = 1,
with the forcing term f(t) given by:
f(t) =
2t, if 0 ≤ t < 1,
1, if 1 ≤ t < 3,
0, if t ≥ 3.
Find X(s) = L{x(t)}(s), the Laplace transform of the solution. Do not solve for x.