Question

ke termine the er t For what Rwll the circuit be 1 Component of the v2 (t) respnsef th input signal is αχ(t) = 20 sin@st).

Answer 1

In s - domain, using voltage divider rule, V_2 (S) = V_i (S) times R/SL + 1/SC + R V_2 (S)/V_i (S) = S C R/S^2 L C + S C R + 1 = S C R/L C[S^2 + s C R/L C + 1/L C] = S times R/L/S^2 + S R/L + 1/L C G (S) = S R/S^2 + 5 R + 50 characteristic equation : S^2 + S R + 50 = 0 S^2 + 2 epsilon w_n S + u_n^2 = 0 w_n^2 = 50 implies w_n = squareroot 50 rad/se if circuit is wonder damped epsilon = 0.5 2 epsilon w_n = R implies R = 2 times 0.5 times squareroot 50 = 7.071 ohm R almostequalto 7 ohm \r\n C) w = 15 rad/sec X_L = W_L = 15 ohm X_C = 1/WC = 3.333 ohm using voltage divider rule V_2 = 20 angle 0 degree times R/R + j X_L - J X_C =