Please show your work in detailed steps.

\f4) An external source feeds an oscillating current of I (t) 2 I0 cos(wt) into the top branch of the circuit shown below (and the same current exits from the bottom branch). As a result, the three circuit elements will have an oscillating potential difference V(t) = V0 cos(wt (,6) across them. Note that all three are in parallel, so the potential difference across all three is the same. Label the current through each of the circuit elements (going from top to bottom) I L (t), I 3(15) and Ic(t). Of course, by charge conservation, it must be true that I(t) IL(t ) -| IR(t ) + IC(t ). a) Given aV(t ), express the charge Q(t) on the top plate of the capacitor 1n terms of V(t ). Now using IC(t )= Q(t ), also express Ig(t) Q(t) in terms of V(t). Be careful about signs (in this as well as in the remaining parts of this problem). b) Express I R( ) in terms of V(t). Now also express I 3(t) in terms of V(t). 0) Finally, express I L( ) in terms of V(t). d) Note that I(t ) IC(t ) -| IR(t) -| IL (15). Substitute your answers from parts a,b and c to rewrite the right-hand side of this expression in terms of V(t) and its derivatives. If you have done everything right, you should have arrived at a differential equation that looks exactly like that of the driven damped oscillator (don't worry that the driving term is a sine instead of a cosine - that will change the phase, but not for the amplitude of oscillations). By comparing the equations, establish a correspondence between the input parameters in this problem (namely I0, V0, L, R, C) and those of the mechanical system (X, 5%, bag, 1/). Using the solution to the mechanical system and making the appropriate substitutions, calculate V0. 6) What is the resonant frequency, at which V5 is maximized? What is V0 at this frequency