1. The problem statement, all variables and given/known data For a series circuit with the following components: 1. Vin(t) 2. 1K resistor 3. 100 mH Inductor 4. 1 uF capacitor 1. Write down the differential eqn. for Vc in the circuit. 2. Solve the DE, calculate the natural and forced response with the following initial conditions: Vc(0) = 0 and dVc(t)/dy = 0 3. Explain the difference between theoretical and experimental results. 2. Relevant equations This was the signal we applied in the lab: Vin(t) = (1V)sin(2∏(2 kHz)t)u(t) 3. The attempt at a solution This is what I have for the DE: dv(t)/dt + (1/RL)Vl(t) + (C/R)d^2Vc(t)/dt^2 = 0 This is for a lab where we have to compare theoretical value to measured value, and apparently they are supposed to be different. I think it's right... but I'm not positive. I'm a little confused because there are 4 different voltages in the circuit (Vl, Vc, Vr, and Vtot), and I'm getting tripped up as to which one I'm solving for. I know that I should take the DE and set it equal to the initial conditions in order to solve for the forced and natural responses, but I really need a little push here to get started. Any help would be appreciated. Thanks.