For a mechanical engineering course in controls, I was asked to
Write the differential equation, state equation, and transfer function for this circuit
That's the full text of the problem, and the schematic below is the extent of the other information given)
I assume \$y\$ is the intended output of the system, but beyond that I'm at a loss as to how to go about this (and of course we've done no example problems with circuits [or, indeed, any example problems at all, really]). I tried playing around with Kirchhoff's laws, which I think works out as follows:
\$\ V1 = V_{R_1} + V_{R_2} + y = V_{R_1} + V_{C_1} \$
\$\ i_{R_1} = i_1 + i_2\$
\$\ V_{R_1}/R_1 = Cdv/dt + i_2 \$ (but I can't figure out how to find i2)
I'm a mechanical engineer and have next to no grasp of circuit theory. I think I can deal with the state equation and transfer function half of the problem, but to get there I need to figure out how to get the differential equation. Any insight would be appreciated.