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For Figure P4.31, the equilibrium position corresponds to

System Dynamics | 3rd Edition | ISBN: 9780073398068 | Authors: William J Palm III ISBN: 9780073398068 208

Solution for problem 4.31 Chapter 4

System Dynamics | 3rd Edition

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System Dynamics | 3rd Edition | ISBN: 9780073398068 | Authors: William J Palm III

System Dynamics | 3rd Edition

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Problem 4.31

For Figure P4.31, the equilibrium position corresponds to x = 0. Neglect the masses of the pulleys and assume that the cable is inextensible, and use conservation of energy to derive the equation of motion in terms of x.

Step-by-Step Solution:

Problem 4.31

For Figure P4.31, the equilibrium position corresponds to x = 0. Neglect the masses of the pulleys and assume that the cable is inextensible, and use conservation of energy to derive the equation of motion in terms of x.

Step by step solution

Step 1 of 3

Due to the arrangement of the pulley,if mass moves by distance ,the mass  moves by distance  

Thus,the velocity of mass  is

The velocity of mass  is

The total kinetic energy is

Substituting the values of velocities,we get

Step 2 of 3

Chapter 4, Problem 4.31 is Solved
Step 3 of 3

Textbook: System Dynamics
Edition: 3
Author: William J Palm III
ISBN: 9780073398068

This textbook survival guide was created for the textbook: System Dynamics, edition: 3. System Dynamics was written by and is associated to the ISBN: 9780073398068. This full solution covers the following key subjects: . This expansive textbook survival guide covers 13 chapters, and 752 solutions. Since the solution to 4.31 from 4 chapter was answered, more than 1223 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 4.31 from chapter: 4 was answered by , our top Engineering and Tech solution expert on 01/03/18, 09:39PM. The answer to “For Figure P4.31, the equilibrium position corresponds to x = 0. Neglect the masses of the pulleys and assume that the cable is inextensible, and use conservation of energy to derive the equation of motion in terms of x.” is broken down into a number of easy to follow steps, and 39 words.

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For Figure P4.31, the equilibrium position corresponds to