Question

2) For a system with the transfer function H(s) =- (st100) c) find the unit impulse response of the system. d) if the input of the system is 3e u(t), what is the output of the system in the frequency domain if all initial conditions are zero. e) if the input of the system is 3e" 100u(t), what is the output of the system in the time domain if all initial conditions are zero. f) what is the frequency of the system?

Answer 1

Given x(t) = 3e^-100 t u(t) X(s) = 3/s + 100 Y(s) = H(s) . X(s) = s + 100/(s + 1)(s + 10) - 3/(s + 100) Y(s) = 3/(s + 1)(s + 10) implies in frequency domain Y(s) = A/s + 1 + B/s + 10 A = 3/(s + 1)(s + 10) * (s + 1) Vertical-bar _s = -1 = 3/9 = 1/3 B = 3/(s + 1)(s + 10) * (s + 10) Vertical-bar _s = -10 implies 3/-9 = -1/3 Y(s) = 1/3(s + 1) - 1/3(s + 10) Apply Inverse Laplace transform we get y(t) = 1/3 e^-t - 1/3 e^-10 t in time domain frequency of system is from the transfer function (s + 1)(s + 10) implies s^2 + 11s + 100 Here �s� co-efficient 11 is taken as frequency 2) H(s) = s + 100/(s + 1)(s + 10) c) unit impulse response of the system H(s) = A/s + 1 + B/s + 10 A =