(Solved): QUESTION: note: solve by using matlab Consider the spring-mass-damper system on a cart, which was ...

QUESTION:

note: solve by using matlab

Consider the spring-mass-damper system on a cart, which was used in the Practice session in Week 02 . Assume \( m=10 \mathrm{~kg}, b=12 \mathrm{Ns} / \mathrm{m} \), and \( k=120 \mathrm{~N} / \mathrm{m} \). Answer the following questions. 1. Create a transfer function ( \( t f \) ) object of this system using tf command. Convert the tf object into a state-space representation using ss command. 2. Using step command, plot the step response of the system. From the step response plot, find the maximum overshoot, peak time, rise time and settling time 3. Compare them with those values computed from the characteristic polynomial of the system 4. Do you find any difference between the values found from the step response and ones from the characteristic polynomial? Explain the difference.