A uniform rod of mass M and length L is free to swing back and forth by pivoting a distance x from its center. It undergoes harmonic oscillations by swinging back and forth under the influence of gravity. Randomized Variables M = 2.4 kg L = 1.6 m x = 0.38 m a) In terms of M, L, and x, what is the rod’s moment of inertia I about the pivot point. b) Calculate the rod’s period T in seconds for small oscillations about its pivot point. c) In terms of L, find an expression for the distance xm for which the period is a minimum.
A uniform rod of mass M and length L is free to swing back and forth by pivoting a distance x from its center. It undergoes harmonic oscillations by swinging back and forth under the influence of gravity. Randomized Variables M = 2.4 kg L = 1.6 m x = 0.38 m a) In terms of M, L, and x, what is the rod’s moment of inertia I about the pivot point. b) Calculate the rod’s period T in seconds for small oscillations about its pivot point. c) In terms of L, find an expression for the distance xm for which the period is a minimum.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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A uniform rod of mass M and length L is free to swing back and forth by pivoting a distance x from its center. It undergoes harmonic oscillations by swinging back and forth under the influence of gravity.
Randomized Variables
M = 2.4 kg
L = 1.6 m
x = 0.38 m
a) In terms of M, L, and x, what is the rod’s moment of inertia I about the pivot point.
b) Calculate the rod’s period T in seconds for small oscillations about its pivot point.
c) In terms of L, find an expression for the distance xm for which the period is a minimum.
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