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Need help to solve this problem using the state variable method

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ADGAN

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Hello everybody, I need help to solve this problem. I'm not getting the correct answer. The answer should be x(0) = x(2T) = I/3(e3/2T – 1)/(e7/2T – 1) and x(T) = I/3(e7/2T-e2T)/(e7/2T-1). I tried this but not getting the denominator.

The switch is periodically opened and closed at T second intervals so that the circuit is in the repetitive steady-state with a period of 2 T. Let R = 1Ω and L = 1H. Assume x (t) = iL(t) and use state-variable methods to determine the value of inductor Current at the instants of switching.

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Reference: Basic Electrical Engineering By Cathey
 
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