A system with input x$($t$)$ and output y$($t$)$ is described by the following differential

equation

d$2$y$($t$)$

dt$2+5$

dy$($t$)$

dt

$+6$y$($t$)=$ x$($t$)$

a$)(4$ marks$)$ Assuming that the above represents a linear time$-$invariant system, find its impulse

response.

b$)(3$ marks$)$ If x$($t$)$ is a periodic signal with time$-$period T defined by u$($t $+$ T$1)$ u$($t $$ T$1)$

between $$

T

$2$

$$ t $$

T

$2$

$,$ determine y$($t$).$