Determine the undamped natural frequency ωn, the damping ratio ζ, and the damped natural frequency ωd.

Consider the single-degree-of-freedom system shown in Figure 5.42.

a. Determine the undamped natural frequency ωn, the damping ratio ζ, and the damped natural frequency ωd.

b. Assume f(t) = 0. Find the free vibration response of the system subjected to the initial conditions x(0) = 0 m and (0) = 1 m/s.

c. Write a MATLAB m-file to plot the system’s response obtained in Part (b).

d. Construct a SimulinkR block diagram based on the differential equation of motion of the system and find the free vibration response.

e. Build a SimscapeR model of the physical system and find the free vibration response.

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