1. The problem statement, all variables and given/known data I have the LCR circuit attached below. At time t=0 the capacitor is uncharged and the switch is closed. By solving an appropriate differential equation, show that the current through the resistor is oscillatory provided L<4CR2. By considering the boundary conditions at t=0 and as t→∞, sketch the form of this current as a function of time. 2. Relevant equations V=IR, V=LdI/dt, V=Q/C. 3. The attempt at a solution So the first bit is pretty simple, giving a DE of LCRd2I/dt2+LdI/dt+RI=V0. Solving for the transient complentary functions using the quadratic formula gives the required condition for an oscillatory current. I can solve the DE to obtain I=exp(-t/2CR)(Asinβt+Bcosβt)+(V0/R), where β=[√(4LCR2-L2)]/2LCR and we are assuming oscillatory solutions do exist as the question wants. I have the initial condition Q=0 for the capacitor when t=0, so then I=0. Then B=-V0/R. However the condition as t→∞ is problematic. I expect I→Vo/R (the steady-state solution) as t→∞. If I let t tend to infinity in my solution, the CF vanishes, so it doesn't allow me to implement any sort of condition. I can only think of this meaning I can let A be zero but I don't think that would be ok. Any clues would be great, thanks!