Question

Consider the RLC circuit in Fig. 5, based on the differential equation relating x() and y() that you obtained from the pre-lab exereise, f -0.2H, C-04F and R-52. i. Plot the zero-input response if y(0)- 1 and y (0)-8 i. Plot the total output response y() if the input signal is [3sin()+2co)), with y(0)= l and y'(0)= 8; Label your plots properly. x(t) Ф R y(t) Fig. 5 RLC circuit network with a shunt capacitor

Need the matlab code for plots

Answer 1

2c = c. d Forall/dt z^. F = y/F z^. L = z^. c z^. R x (t) = y (t) = L . d 2L/dt x (t) - y (t) - Lc d^t H/d + L/R dy/dt LC d^2 y/dt^2 + C/R dy/dt + y (t) = x (t) 0.08 d^2 y/dt^2 + 0.04 dy/dt + y (t) = 0 d^2 y/dt^2 + 0.5 dy/dt + 12.5 y = 0 y (t) = e^-0.25 t [A < B (3.53 t) + B sin (3.53 t)] y (0) = 1 Then A = 1 y_n (t) = e^-0.25 t [cos (3.53 t) + B sin 3.53 t] \r\n Apply Condition y� (0) = 8 B = 8 + 2.5/3.53 = 2.34 y_L (t) = e^-0.25 t [cos (3.53 t) + 2.34 sin (3.53 t)] zero input Response y n (t) Now (2 (14) 2 the particular solution: - x (t) = sin (n t) + cos (kt) 4 (t) Let