Determine the dynamic amplitude X and the static deflection xst of the system.

 

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

a. Assume f(t) = 500sin(60t) and initial conditions x(0) = 0 and (0) = 0. Determine the dynamic amplitude and the static deflection xst of the system. Find the forced vibration response of the system.

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

c. Construct a Simulink block diagram based on the differential equation of motion of the system and find the forced vibration response.

d. Build a Simscape model of the physical system and find the forced vibration response.

e. Assume that the driving frequency varies from 0 to 100 rad/s. Write a MATLAB m-file to plot the dimensionless ratio X/xst versus the frequency ratio ω/ωn

 

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erive the differential equations in terms of the liquid heights h1 and h2.

  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….

Derive the differential equation relating the liquid height h and the volume flow rate qi at the inlet.

  Consider the single-tank liquid-level system shown in Figure 7.19, where the volume flow rate into the tank through a pipe is qi. The liquid leaves the tank through an orifice….

Derive the differential equations in terms of the liquid heights h1 and h2.

Figure 7.20 shows a hydraulic system of two interconnected tanks that have the same cross-sectional area of A. A pump is connected to tank 1. Assume that the relationship between the….