Problem $3$

An analog system is characterized by the impulse response h$($t$)$ depicted in Figure $3$a:

Figure $3$a: System and Impulse Response

We wish to find the output y$($t$)$ when the input is the signal x$($t$)$ depicted in Figure $3$b$.$

$3$ay$($t$)=$tu$($t$)-($t$-2)$u$($t$-2).$ Find this output signal using the Laplace transform approach.