Consider an RLC circuit with R = 5 Ohms, L= ½ H, C= 2/9 F and input voltage e(t) = exp(-t/2)
a. Starting from KVL show that the DE for the voltage across R is given by: v'' + 10 v' + 9 v = -5 exp(-0.5 t)
b. Find vc in terms of the arbitrary constants C1 and C2
c. Find vp
d. Add vc and vp and use the initial conditions If v(0) = 0 and v'(0) = -5 to show that the actual solution is
v(t) = 0.625*exp(-1.0*t)+0.551*exp(-9.*t)-1.18*exp(-0.500*t)
e. Use Matlab to plot the solution