plot the two angular displacements θ1 and θ2 corresponding to the two sets of initial conditions versus 0 ≤ t ≤ 10 in the same graph.

 

The pendulum system in Figure 8.35 consists of a uniform thin rod of length and a concentrated mass at its tip. The friction at the pivot causes the system to be damped. When the angular displacement θ is not very small, the system is described by the nonlinear model

 

Assume, in consistent physical units, that ml2 = 1.5 ,  = 6.8. Two sets of initial conditions

are to be considered: (1) θ(0 )  = 10°, ( 0)  = 0 , and (2) θ(0) = 20 °, (0) = 0. Using the RK4 method plot the two angular displacements θ1 and θ2 corresponding to the two sets of initial conditions versus 0 ≤ ≤ 10 in the same graph. Angle measures must be converted to radians.

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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….