Explanation Definition: An object is in simple harmonic motion if its displacement y at time t is modeled by y = a sin ⁡ ω t or y = a cos ⁡ ω t . In general, the cosine functions representing harmonic motion may be shifted horizontally or vertically. In this case, the equations take the form y = a sin ⁡ ω t - c + b or y = a cos ⁡ ω t - c + b . Then, frequency = ω 2 π . Any sine curve can be expressed in the following equivalent forms: y = A sin ⁡ k t - b , the phase is b . For the curves, y 1 = A sin ⁡ k t - b and y 2 = A sin ⁡ k t - c , the phase difference between y 1 and y 2 is b - c . If the phase difference is a multiple of 2 π , the waves are in phase; otherwise, the waves are out of phase. Calculation: Given y 1 = 5 sin ⁡ 2 t - 1 . y 1 = 5 sin ⁡ 2 t - 1 2 Compare with y = a sin ⁡ ω t - c + b . a = 5 and ω = 2 . Frequency = ω 2 π = 2 2 π = 1 π . Given y 2 = 5 sin ⁡ 2 t - 3

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN: 9781305071742

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 6.CR, Problem 13CC

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Whether the given functions have the same frequency, the phase for each equation, phase difference and whether the objects are moving in phase or out of phase.

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Chapter 6.CR, Problem 12CC

Chapter 6.CR, Problem 1E

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Algebra and Trigonometry (MindTap Course List)

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Whether the given functions have the same frequency, the phase for each equation, phase difference and whether the objects are moving in phase or out of phase.

Solution Summary: The author explains that the cosine functions representing harmonic motion may be shifted horizontally or vertically.

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Whether the given functions have the same frequency, the phase for each equation, phase difference and whether the objects are moving in phase or out of phase.

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Chapter 6 Solutions