Consider a source-free parallel RLC circuit having alpha =10^8 s^-1, omega-sub-zero = 10^3 rad/s, and omega-sub-zero * L = 5 ohm.
a) Show that the stated units of omega-sub-zero * L are correct.
b) Compute s_1and s_2.
c) Write the general form of the natural response for the capacitor voltage.
d) By appropriate substitution, verify that the answer in part (c) is indeed a solution to Eq.[1] if the inductor and capacitor each initially store 1mJ of energy, respectively.