 #1
 32
 0
Homework Statement
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.
Homework Equations
Y(s)=Y_{zs}(s) + Y_{zi}(s)
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
Attachments

3.9 KB Views: 419

1.8 KB Views: 365

19 KB Views: 362