Explanation Calculation: Write the expression for the period of oscillation: τ n = 4 l g ∫ 0 π 2 ( d ϕ 1 − sin 2 ( θ m 2 ) sin 2 ϕ ) . (1) Consider the below term in equation (1). 1 1 − sin 2 ( θ m 2 ) sin 2 ϕ Applying the binomial theorem, 1 1 − sin 2 ( θ m 2 ) sin 2 ϕ = [ 1 − sin 2 ( θ m 2 ) sin ϕ ] − 1 / 2 = 1 + 1 2 sin 2 θ m 2 sin 2 ϕ + .... (2) Neglecting term of order higher than 2. Apply equation (2) in equation (1). τ n = 4 l g ∫ 0 π 2 ( 1 + 1 2 sin 2 θ m 2 sin 2 ϕ ) Take sin 2 ϕ = 1 2 ( 1 − cos 2 ϕ ) , Substitute 1 2 ( 1 − cos 2 ϕ ) for sin 2 ϕ

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

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

Publisher: McGraw-Hill Education

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Free Damped Vibrations

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Chapter 19.1, Problem 19.33P

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Show that the period of a simple pendulum of length l may be approximated by the formula τ=2πlg(1+14sin2θm2).

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Chapter 19.1, Problem 19.32P

Chapter 19.1, Problem 19.34P

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Chapter 19 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.2P Ch. 19.1 - Prob. 19.3P Ch. 19.1 - Prob. 19.4P Ch. 19.1 - Prob. 19.5P Ch. 19.1 - Prob. 19.6P Ch. 19.1 - Prob. 19.7P Ch. 19.1 - Prob. 19.8P Ch. 19.1 - Prob. 19.9P Ch. 19.1 - Prob. 19.10P

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Show that the period of a simple pendulum of length l may be approximated by the formula τ = 2 π l g ( 1 + 1 4 sin 2 θ m 2 ) .

Solution Summary: The author illustrates how the period of a simple pendulum of length l may be approximated by the formula tau =2pi

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Show that the period of a simple pendulum of length l may be approximated by the formula τ=2πlg(1+14sin2θm2).

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Chapter 19 Solutions