3. Laplace transform method to model an RLC network
Consider an RLC network subject to a unit impulse δ(t − π), whichcan be described by
d2q(t) + 14dq(t) + 1010q(t) = δ(t − π), dt2 dt
where q(t) is the system response, the charge on the capacitorat time t. The initial current isi(0) = 9 and the initial charge isq(0) = 0.
(a) Find q(t). Express your solution explicitly – without use ofany special functions.
(b) Plot your answer using MATLAB. Interpret q(t) with respectto the impulse and the initial conditions: that is, identify inyour plot which part of your solution is due to δ(t
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