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1. For the following network:
a. Find the differential equation assuming that v(t) is the input and the charge on the capacitor q(t) is the output. Hints: iR1= (iR2 + iL), iR2 = (vL + vC) / R2, iL = iC = dq/dt and page 114.
b. Find the state-space representation. Give your answer in vector-matrix form assuming the following values L = 1 H, C = 1 F and R1 = R2 = 1 Ω.
Represent the following transfer function in state space. Give your answer in vector-matrix form.
Extra credit: Find the transfer function G(s) = Y(s) / R(s) for the following system represented in state space.
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Q. Determine the Laplace transform for each of the following functions from the basic de?nition of Equation. (a) f 1 (t) = u(t) (b) f 2 (t) = e-at (c) f 3 (t) = df (t) dt,
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