Consider the circuit shown in Figure P4.55. a. Write the differential equation for v(t). b. Find the time constant and the form of the complementary solution. c. Usually, for an exponential forcing...

Consider the circuit shown in Figure P4.55.

a. Write the differential equation for v(t).

b. Find the time constant and the form of the complementary solution.

c. Usually, for an exponential forcing function like this, we would try a particular solution of the form v_p
( t )=Kexp( −10t ). Why doesn’t that work in this case?

d. Find the particular solution. [Hint: Try a particular solution of the form v_p
( t )= Ktexp( −10t ).]

e. Find the complete solution for v(t).