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Description: A uniform rod of mass M and length L is pivoted about one end and oscillates in avertical plane. Where should one place a mass m=M so that the frequency of theharmonic motion remains unchanged?LmM.2L/3L/23L/8L/3

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A uniform rod of mass M and length L is pivoted about one end and oscillates in a vertical plane. Where should one place a mass m=M so that the frequency of the harmonic motion remains unchanged?

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter16: Oscillations

Section: Chapter Questions

Problem 28PQ: We do not need the analogy in Equation 16.30 to write expressions for the translational displacement...

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Concept explainers

Simple harmonic motion

Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.

Simple Pendulum

A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.

Oscillation

In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.

Topic Video

Question

A uniform rod of mass M and length L is pivoted about one end and oscillates in a
vertical plane. Where should one place a mass m=M so that the frequency of the
harmonic motion remains unchanged?
L
m
M.
2L/3
L/2
3L/8
L/3

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