Problem 3 For the mechanical m-b-k system shown below, x(t) b f(t) m www where the force f(t) is the input and displacement x(t) is the output. Assume zero initial conditions and with the parameters tabulated in the table, m (kg) b (Ns/m) k (N/m) F (N) F (N/s) 3 2 8 20 1 a (3) Obtain the proper transfer function (only one transfer function) G(s) according to the given input and output. b (2) Determine the order of the system. If the system is 1" order determine the time constant and gains K. If the system is 2nd oder determine the undamped natural frequency w damping ratio (and gains K.. c (3) Plot the response of the system to the step input f(t) = F1(t). Calculate the (a) peak time tp, (b) steady-state response = y(t), (c) settling time t,(+2), and (d) maximum overshoot M,(%) d (2) Plot the response of the system to the impulse input f(t) = Fo(t) (t> 0) and calculate the steady-state response x, y(too) to this input. =