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 ) Where, θ m is the amplitude of oscillation. Using the binomial theorem, we can write the above formula as: 1 1 − sin 2 ( θ m 2 ) sin 2 ϕ = [ 1 − sin 2 ( θ m 2 ) sin 2 ϕ ] − 1 / 2 = 1 + 1 2 sin 2 θ m 2 sin 2 ϕ + ..... Neglecting terms of the order higher than 2 and setting sin 2 ϕ = 1 2 ( 1 − cos 2 ϕ ) thus, τ n = 4 l g ∫ 0 π / 2 { 1 + 1 2 sin 2 θ m 2 [ 1 2 ( 1 − cos 2 ϕ ) ] } d ϕ τ n = 4 l g ∫ 0 π / 2 { 1 + 1 4 sin 2 θ m 2 − 1 4 sin 2 θ m

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Chapter 19.1, Problem 19.33P

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To show that the period of a simple pendulum of length l is approximated by the given formula:

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Chapter 19.1, Problem 19.32P

Chapter 19.1, Problem 19.34P

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Chapter 19 Solutions

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To show that the period of a simple pendulum of length l is approximated by the given formula:

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