# Need help simplifying equation to find the laplace transform of it

there are two loops in an electrical circuit. ive got two equations and two unknowns.
here are the equations

v(t) = I1*R1 + 1/c*int(I1*dt) - 1/c*int(I2*dt) - first loop
0 = LdI2/dt + R2*I2 - 1/c*int(I1*dt) + 1/c*int(I2*dt) - second loop

the capacitor is in the branch between the two loops.

Im drawing a blank on this. I need to simplify into one equation so I can find the laplace transform of the one equation.
the goal is to find the step response of the system using matlab.

Related Introductory Physics Homework Help News on Phys.org
Tom Mattson
Staff Emeritus
Gold Member
You'll want to differentiate both equations first, to get rid of those god awful integrals.

I need to simplify into one equation so I can find the laplace transform of the one equation.
There's nothing wrong with taking the Laplace transform first and then simplifying.

can i get a confirmation that i set up those differential equations properly? im having some trouble with this still. if i differentiate, than i get derivative of the input. im trying to find the output voltage which is across the R2 resistor.

im still having trouble with this problem. ive tried multiple methods including differentiation and solving for a variable and plugging it into the first equation but im still where i started the other day. im trying to find an eqation that relates the output voltage across R2 to the input. im confident my beginning equations are correct, but i dont know where to go from there.