Explanation Given : The below representation of rotational system: - Fig.(b) Concept Used: Apply Alembert’s principle for rotational system to obtain the equation of motion. According to the Alembert’s principle for the rotational system, the externally applied torque is equal to the combined torque applied internally in the system. The given system uses gear train and does not have lossless gears. All of the gears have inertia and for some shafts there is a viscous friction. Thus, to obtain the transfer function, we need to reflect all the impedances to the input shaft θ 1 . And the gear ratio is not the same for impedances. By utilizing the equation of motion obtain the required transfer function G ( s ) = θ 1 ( s ) T ( s ) Calculation: From the given representation of rotational system, we can observe that the given system uses gear train and does not have lossless gears. All of the gears have inertia and for some shafts, there is a viscous friction. Thus, to obtain the transfer function, we need to reflect all of the impedances to the input shaft θ 1 . The gear ratio is not the same for impedances. Like D is reflected only through one gear ratio as D ( N 1 N 2 ) 2 whereas J 4 and J 5 is reflected through two gear ratios as ( J 4 + J 5 ) [ ( N 3 N 4 ) ( N 1 N 2 ) ] 2 . The result of reflecting all impedances to θ 1 is shown in fig. (b), from which the equation of motion is

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ISBN: 9781118170519

Author: Norman S. Nise

Publisher: WILEY

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Forced undamped vibrations

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Chapter 2, Problem 40P

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The transfer function G(s)=θ1(s)T(s) for the given rotational system: -

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Chapter 2, Problem 39P

Chapter 2, Problem 41P

Chapter 2 Solutions

Control Systems Engineering

Ch. 2 - Prob. 1RQ Ch. 2 - Prob. 2RQ Ch. 2 - Prob. 3RQ Ch. 2 - Define the transfer function.Ch. 2 - Prob. 5RQ Ch. 2 - What do we call the mechanical equations written...Ch. 2 - If we understand the form the mechanical equations...Ch. 2 - Why do transfer functions for mechanical networks...Ch. 2 - What function do gears perform?Ch. 2 - What are the component parts of the mechanical...

Ch. 2 - The motor’s transfer function relates armature...Ch. 2 - Summarize the steps taken to linearize a nonlinear...Ch. 2 - Prob. 1P Ch. 2 - Prob. 2P Ch. 2 - Prob. 3P Ch. 2 - Prob. 4P Ch. 2 - Prob. 5P Ch. 2 - Prob. 6P Ch. 2 - Prob. 7P Ch. 2 - A system is described by the following...Ch. 2 - For each of the following transfer functions,...Ch. 2 - Write the differential equation for the system...Ch. 2 - Write the differential equation that is...Ch. 2 - Prob. 12P Ch. 2 - Use MATLAB to generate the MATLAB ML transfer...Ch. 2 - Repeat Problem 13 for the MATLAB following...Ch. 2 - Use MATLAB to generate the partial fraction...Ch. 2 - Use MATLAB and the Symbolic Math Symbolic Math...Ch. 2 - Prob. 17P Ch. 2 - Prob. 18P Ch. 2 - Prob. 19P Ch. 2 - Repeat Problem 19 using nodal equations. [Section:...Ch. 2 - Prob. 22P Ch. 2 - Prob. 23P Ch. 2 - Prob. 24P Ch. 2 - Prob. 25P Ch. 2 - Prob. 26P Ch. 2 - Prob. 27P Ch. 2 - Prob. 28P Ch. 2 - Prob. 29P Ch. 2 - Write, but do not solve, the equations of motion...Ch. 2 - For the unexcited (no external force applied)...Ch. 2 - For each of the rotational mechanical systems...Ch. 2 - For the rotational mechanical system shown in...Ch. 2 - Find the transfer function, 1sTs , for the system...Ch. 2 - For the rotational mechanical system with gears...Ch. 2 - For the rotational system shown in Figure P2.21,...Ch. 2 - Prob. 37P Ch. 2 - Find the transfer function, Gs=4s/Ts , for the...Ch. 2 - For the rotational system shown in Figure P2.24,...Ch. 2 - Prob. 40P Ch. 2 - Given the rotational system shown in Figure P226,...Ch. 2 - In the system shown in Figure P2.27, the inertia,...Ch. 2 - Prob. 43P Ch. 2 - Given the combined translational and rotational...Ch. 2 - Prob. 45P Ch. 2 - The motor whose torque-speed characteristics are...Ch. 2 - A dc motor develops 55 N-m of torque at a speed of...Ch. 2 - 48. In this chapter, we derived the transfer...Ch. 2 - Prob. 49P Ch. 2 - Find the series and parallel analogs for the...Ch. 2 - Find the series and parallel analogs for the...Ch. 2 - A system’s output, c, is related to the system’s...Ch. 2 - Prob. 53P Ch. 2 - Consider the differential equation...Ch. 2 - 55. Many systems are piecewise linear. That is,...Ch. 2 - For the translational mechanical system with a...Ch. 2 - 57. Enzymes are large proteins that biological...Ch. 2 - Prob. 58P Ch. 2 - Figure P2.36 shows a crane hoisting a load....Ch. 2 - 60. In 1978, Malthus developed a model for human...Ch. 2 - 61. In order to design an underwater vehicle that...Ch. 2 - 62. The Gompertz growth model is commonly used to...Ch. 2 - A muscle hanging from a beam is shown in Figure...Ch. 2 - A three-phase ac/dc converter supplies dc to a...Ch. 2 - Prob. 65P

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