Explanation Given information: The period of a simple pendulum of length l is given by, τ = 2 π l g ( 1 + 1 4 sin 2 θ m 2 ) Here, θ m is the amplitude of oscillation. For small oscillations the period is given by the formula: ( τ n ) 0 = 2 π l g But, if the period of the pendulum is 0.5% longer than the period of the same pendulum then, τ n = 1 + 0.5 100 ( τ n ) 0 o r , τ n = 1.0052 π l g By using the given formula the equation can be written as; τ n = ( τ n ) 0 [ 1 + 1 4 ( sin 2 θ m 2 ) ] 1

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

Author: Ferdinand P. Beer, E. Russell Johnston Jr., Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 19.1, Problem 19.34P

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To value of θm if, the period of the pendulum is 0.5% longer than the period of the same pendulum by using the given formula.

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Chapter 19.1, Problem 19.33P

Chapter 19.1, Problem 19.35P

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Can you solve it analytically using laplace transforms and with Matlab code as well please. Thank You

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Vector Mechanics for Engineers: Dynamics

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To value of θ m if, the period of the pendulum is 0.5% longer than the period of the same pendulum by using the given formula.

Solution Summary: The author explains that the amplitude of the oscillation is given by the formula theta_m for a simple pendulum of length l.

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To value of θm if, the period of the pendulum is 0.5% longer than the period of the same pendulum by using the given formula.

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Chapter 19 Solutions