Question

Given the f Specify the choice (no credit ) find the forced response output li. If the input signal is voltage Ct)

Answer 1

H(s) = V_2 (s)/V_1 (s) = s + 4/s^2 + 5s + 6 Specify the type of natural response Under damping, Over damping (or) Critically damping Justify choice. V_2 (s)/V_1 (s) = H(s) = s + 4/s^2 + 5s + 6 Characteristic equation s^2 + 5s + 6 = 0___(1) s^2 + 2 epsilon omega_n s + omega_n^2 = 0___(2) Compare both (1) & (2) omega_n^2 = 6 omega_n = squareroot 6 rad/sec 2 epsilon omega_n = 5 epsilon = 5/2 omega_n = 5/2 squareroot 6 = 2.5/squareroot 6 = 1.0206 > 1 epsilon > 1 Over damped epsilon = 1 Critically damped epsilon < 1 Under damped This is over damped natural response. if the i/p signal V_1 (t) = 10 e^-2t cos (t + 45 degree) find the forced response output voltage V_2 (t) \r\n V_2 (s)/V_1 (s) = s + 4/s^2 + 5s + 6 = s + 4/(s + 2)(s + 3) V_1 (t) = 10 e^-2t cos (t + 45 degree) = 10 e^-2t [cos t cos 45 - sin t sin 45]