An LCR series circuit satisfies the following system dQ dQ dt +R- dt and we will...

  

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An LCR series circuit satisfies the following system d²Q dQ dt² +R- dt and we will assume that t = 0, Q = 0, and t = 0, dQ/dt = 0. Assume that the system is critically damped with L = C = 1 and R=2. Assume that the laplace transform of I(t) is W(s) and Q(t) is Z(s). Assume that we have the strange input function E(t)= Eo exp(-t) sin(t). L + + ¡Q = E(t) Write Q(t) in terms of the unit impulse response function. This requires you to write down the differential equation for the unit impulse response function h(t), take the transform to find H(s), invert to get h(t) and use this to construct y(t). When you write down the integral write out the integral completely but do not evaluate. An LCR series circuit satisfies the following system d²Q dQ dt² +R- dt and we will assume that t = 0, Q = 0, and t = 0, dQ/dt = 0. Assume that the system is critically damped with L = C = 1 and R=2. Assume that the laplace transform of I(t) is W(s) and Q(t) is Z(s). Assume that we have the strange input function E(t)= Eo exp(-t) sin(t). L + + ¡Q = E(t) Write Q(t) in terms of the unit impulse response function. This requires you to write down the differential equation for the unit impulse response function h(t), take the transform to find H(s), invert to get h(t) and use this to construct y(t). When you write down the integral write out the integral completely but do not evaluate.

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