(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Derive the second order differential equation relating x(t) and y(t).

Using the Laplace transform, find the total response as a function of the zero input response and the zero state response in the following form.

2. Relevant equations

Y(s)=Y_{zs}(s) + Y_{zi}(s)

3. The attempt at a solution

Loop1: R_{s}*i_{1}+ 1/c integral(i_{1}+ i_{2}) dt = x_{s}(t)

Loop2: 1/c integral(i_{1}+ i_{2}) dtau + R_{load}*i_{2}+ L di_{2}/dt = 0

Take derivatives

Loop1: R di_{1}/dt + (i_{1}+ i_{2})/C = dx/dt

Loop2: R di_{2}/dt + L di_{2}/dt + (i_{1}+ i_{2})/C = 0

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# Homework Help: RLC Circuit Second Order Differential and Laplace

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