[5+5+10=20pts] (Laplace Transform) a) Express the function
$f(t) = \begin{cases} 1, & 0 \le t < 2 \\ t, & 2 \le t < 3 \\ 2t + 1, & t \ge 3 \end{cases}$
in terms of the unit step function $u_c(t)$ $c > 0$.
b) Find the Laplace transform of $f(t)$.
c) Use the Laplace transform to find the solution of the initial value problem
$y'' = f(t)$, $y(0) = 1$, $y'(0) = 0$,
