## Step Function Laplace Question

Hello,

I need help with the second part of the question.

Firstly i broke down the conditions for the step function, as a linear combination of two step functions. I ended up with:
t- (t-2pi) U 2pi +4pi U 2pi ** where U is the heavyside function.
Working my way with this I took the laplace of both sides and got

Y(s) (s²+16)= 1/s² -e^(2πs)/s² + 4πe^(2πs)/s² +8s+9..

Now I inverse laplace transform the above expression and ended up with the expressions that i submitted.

Thanks !