Problem $1.(30$ pts$)$ Consider the transfer function

$G(s)=\frac{Y(s)}{U(s)}=\frac{10}{(5s+1)(3s+1)}$

What is $y(t)$ for the following inputs?

a$.(10$ pts$)$ Step input of size $M$

b$.(10$ pts$)$ Unit impulse input $(t)$

c$.(10pts)sint$