# Problem 5 (20 Points): For the circuit shown below, the input is the current source, I(t) and the...

###### Question:

Problem 5 (20 Points): For the circuit shown below, the input is the current source, I(t) and the output is eo. 1). Find the state variable model. Take ec and IL as state variables (refer notes from Chapter-6). 2). Apply Laplace Transform on the state variable model (from part-1) and show that the transform of the output (eo) is given by the expression: 사스 ; if the initial conditions, L(0) and ec(0) are known. Note: ec(0)-eo(0) R L R L 3) From part-2, identify the transfer function, H(s), zero-state [Eo(s)]zs and zero-input [Eo(s)]zi transform. 4) From part-3, find the zero-state, [eo(t)]zs and zero-input, [eo(t)la response if C-1 F R-1/5 Ω,L-1/6 H Input, I(t)- 1 +cost. 5). From the result of part-4, identify the steady state, [eo(t)],s and transient, [eo(t)]tr response.

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