Explanation Formula used: Maclaurin expansion of sin x : “The Maclaurin expansion of sin x is given by, sin x = x − x 3 3 ! + x 5 5 ! − x 7 7 ! + ⋯ ” Calculation: Given that, the displacement y = 0.5 sin 0.5 t − 0.2 sin 0.4 t where t is the time in seconds. Replace x by 0.5 t in the Maclaurin expansion of sin x and obtain the Maclaurin expansion of sin 0.5 t as follows. sin ( 0.5 t ) = 0.5 t − ( 0.5 t ) 3 3 ! + ( 0.5 t ) 5 5 ! − ⋯ = 0.5 t − 1 6 ( 0.5 t ) 3 + 1 120 ( 0.5 t ) 5 − ⋯ Similarly replace x by 0.4 t in the Maclaurin expansion of sin x and obtain the Maclaurin expansion of sin 0.4 t as follows. sin ( 0.4 t ) = 0.4 t − ( 0.4 t ) 3 3 ! + ( 0.4 t ) 5 5 ! − ⋯ = 0.4 t − 1 6 ( 0.4 t ) 3 + 1 120 ( 0.4 t ) 5 − ⋯ Obtain the Maclaurin series of displacement y as shown below. y = 0.5 sin 0.5 t − 0.2 sin 0.4 t = 0.5 ( 0.5 t − 1 6 ( 0.5 t ) 3 + 1 120 ( 0.5 t ) 5 − ⋯ ) − 0

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

11th Edition

ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Chapter 30, Problem 72RE

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The first three terms of Maclaurin series for displacement y of a water wave.

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Chapter 30, Problem 71RE

Chapter 30, Problem 73RE

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Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

Ch. 30.1 - Prob. 1PE Ch. 30.1 - Prob. 2PE Ch. 30.1 - Prob. 1E Ch. 30.1 - Prob. 2E Ch. 30.1 - Prob. 3E Ch. 30.1 - Prob. 4E Ch. 30.1 - Prob. 5E Ch. 30.1 - Prob. 6E Ch. 30.1 - Prob. 7E Ch. 30.1 - Prob. 8E

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