Part (a) In terms of M, L, and x, what is the rod's moment of inertia I about the pivot point. Expression : Select from the variables below to write your expression. Note that all variables may not be required. a, ß, 0, a, d, g, h, j., k, L, M, n, P, t, x Part (b) Calculate the rod's period T in seconds for small oscillations about its pivot point. Numeric : A numeric value is expected and not an expression. T =\,932 Part (c) In terms of L, find an expression for the distance xXm for which the period is a minimum. Expression : Xm = Select from the variables below to write your expression. Note that all variables may not be required. a, ß, 0, a, d, g, h, j, k, L, M, n, P, t, x

Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter12: Coupled Oscillations
Section: Chapter Questions
Problem 12.22P
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Please answer question 6

Problem 6: 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 = 4.8 kg
L = 1.6 m
x = 0.42 m
Part (a) In terms of M, L, and x, what is the rod's moment of inertia I about the pivot point.
Expression :
I =
Select from the variables below to write your expression. Note that all variables may not be required.
a, B, 0, a, d, g, h, j, k, L, M, n, P, t, x
Part (b) Calculate the rod's period T in seconds for small oscillations about its pivot point.
Numeric : A numeric value is expected and not an expression.
T =
1,932
Part (c) In terms of L, find an expression for the distance x,m for which the period is a minimum.
Expression :
Xm =
Select from the variables below to write your expression. Note that all variables may not be required.
a, B, 0, a, d, g, h, j, k, L, M, n, P, t, x
Transcribed Image Text:Problem 6: 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 = 4.8 kg L = 1.6 m x = 0.42 m Part (a) In terms of M, L, and x, what is the rod's moment of inertia I about the pivot point. Expression : I = Select from the variables below to write your expression. Note that all variables may not be required. a, B, 0, a, d, g, h, j, k, L, M, n, P, t, x Part (b) Calculate the rod's period T in seconds for small oscillations about its pivot point. Numeric : A numeric value is expected and not an expression. T = 1,932 Part (c) In terms of L, find an expression for the distance x,m for which the period is a minimum. Expression : Xm = Select from the variables below to write your expression. Note that all variables may not be required. a, B, 0, a, d, g, h, j, k, L, M, n, P, t, x
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