Assume a causal LTI system S1 is described by the following differential equation: \frac{d^{2} y(t)}{d t^{2}}+4 \frac{d y(t)}{d t}+3 y(t)=a x(t), \quad y(0)=0, y^{\prime}(0)=0 where a is a constant. Moreover,

we know that when the input is e', the output of the system (5 pts) Find the transfer function H1(s) of the system. (The answer should not be in terms of a, i.e., you should find the value of a). (5 pts)Find the output y(t) when the input is x(t) = u(t). (6 pts) The system S1 is linearly cascaded with another causal LTI system S2. Thesystem S2 is given by the following input-output pair: \mathcal{S}_{2} \text { input : } u(t)-u(t-1) \rightarrow \text { output }: \tau(t)-2 \tau(t-1)+\tau(t-2) Find the overall impulse response.