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Engineering and Tech / System Dynamics 3 / Chapter 4 / Problem 4.82

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

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QUESTION:

Obtain the equations of motion for the system shown in Figure P4.82 for the case where \(m_{1}=m_{2}=m\). The cylinder is solid and rolls without slipping. The platform translates without friction on the horizontal surface.

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QUESTION:

Obtain the equations of motion for the system shown in Figure P4.82 for the case where \(m_{1}=m_{2}=m\). The cylinder is solid and rolls without slipping. The platform translates without friction on the horizontal surface.

ANSWER:

Step 1 of 4

Consider a free body diagram of the cylinder where the displacement is measured from the equilibrium position. And assume that the displacement is greater than .

Consider the platform is stationary relative to the rolling cylinder.

Write the equation of motion of the linear motion of cylinder using FBD of figure.

As the cylinder does not slip. Then,

is the cylinder rotational angle.

It is known that

Substitute for in equation (2)

Differentiate the above equation,

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