The weightless rod carries two masses m, one at a distance L from the pivot o the other at 2L. If the rod is rotated by a small angle e and released, determine the following: a. the differential equation of motion of the system, and p. the natural frequency of vibration of the rod.

The weightless rod carries two masses m, one at a distance L from the pivot o the other at 2L. If the rod is rotated by a small angle e and released, determine the following: a. the differential equation of motion of the system, and p. the natural frequency of vibration of the rod.

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter5: Three-dimensional Equilibrium

Section: Chapter Questions

Problem 5.15P: In Sample Problem 5.5, determine Oy with one scalar equilibrium equation.

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Concept explainers

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.

Question

2. The weightless rod carries two masses m. one at a distance L from the pivot or
the other at 2L. If the rod is rotated by a small angle e and released,
determine the following:
a. the differential equation of motion of the system, and
b. the natural frequency of vibration of the rod.
(J. - mc?, where c dist amce
from mass m to pivot 0.)

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