Figure 7.18 shows a liquid-level system in which two tanks have cross-sectional areas A1 and A2, respectively. The volume flow rate into tank 1 is qi. A pump is connected to the bottom….

## 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 ω_{n}, the damping ratio ζ, and the damped natural frequency ω_{d}.

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.