Consider the RLC circuit in Figure 1.

Answer the following questions using the values of vin (t), C and L as follows: v_{\text {in }}(t)=10(d+1) \mathrm{V}, C=(c+5) \mu \mathrm{F}, L=(b+2) (a) Calculate the equivalent impedance of the circuit as seen from the battery source. \text { Derive the differential equiation that relates } v_{c}(t) \text { to } v_{i n}(t) \text {. } \text { Derive the differential equation tht relat an ent } i_{1}(t) \text { to } v_{i n}(t) \text {. } \text { Find the steady state voltage across the capaacitor as } t \text { tends to infinity. }