The suspension system for one wheel of an oldfashioned picku

The suspension system for one wheel of an old-fashioned pickup truck is illustrated in figure below. The mass of the vehicle supported by tire m_1 = 500 kg and the mass of the wheel is m_2 = 15 kg. The suspension spring has a spring constant k_1 35,000 N/m, and the tire has a spring constant k_2 = 60,000 N/m. The damping constant of the shock absorber is b = 7, 500 N-s/m. Draw the system diagram with input and output in it. Write two equations of motion for the suspension system. Obtain the transfer function G(s) = Y_1(s)/X(s) in the simplest form which represents the vehicle response to bumps in the road. Plot the system output y_1(t), if system input is a unit step function and all initial conditions are zero, and label and title the plot, (using step(transfer function)) Estimate the settling time T_s peak time T_P, and OS%, and tell the nature of system output response, (using step info(transfer function)) Mark settling time T_s, peak time T_P, and OS% on the plot.

Solution

The answer of following question is as follows.

The maximum mark settling time is 8 min .

While the peak time is 7 min.