Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Question
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Chapter 5, Problem 129RE
To determine

To calculate: The amplitude of the oscillations of the weight.

Expert Solution & Answer
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Answer to Problem 129RE

The required amplitude is (1.5)2+(0.5)2 .

Explanation of Solution

Given information:

The model: y=1.5sin8t−0.5cos8t

Calculation:

Given the equation of displacement of the harmonic system is:

  y=1.5sin8t−0.5cos8t..............(1)

To find the amplitude of the equation (1), change the equation to the form of y=a2+b2sin(Bt+C) .

Multiply and divide the right hand side of the equation (1) by the square root of the sum of the squares of the amplitude of the trigonometric part that is, (1.5)2+(0.5)2 and simplify.

  y=(1.5)2+(0.5)2(1.5)2+(0.5)2(1.5sin8t−0.5cos8t)y=(1.5)2+(0.5)2(1.5(1.5)2+(0.5)2sin8t−0.5(1.5)2+(0.5)2cos8t)y=(1.5)2+(0.5)2(sin(8t−cos−1(1.5(1.5)2+(0.5)2)))

Here, the amplitude of the sine function is 1.

So, substitute 1 for (sin(8t−cos−1(1.5(1.5)2+(0.5)2))) in the above expression.

  y=(1.5)2+(0.5)2⋅(1)=(1.5)2+(0.5)2

Hence, the required amplitude is (1.5)2+(0.5)2 .

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Chapter 5, Problem 128RE
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Chapter 5, Problem 130RE

Chapter 5 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
Ch. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Prob. 35ECh. 5.1 - Prob. 36ECh. 5.1 - Prob. 37ECh. 5.1 - Prob. 38ECh. 5.1 - Prob. 39ECh. 5.1 - Prob. 40ECh. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - Prob. 51ECh. 5.1 - Prob. 52ECh. 5.1 - Prob. 53ECh. 5.1 - Prob. 54ECh. 5.1 - Prob. 55ECh. 5.1 - Prob. 56ECh. 5.1 - Prob. 57ECh. 5.1 - Prob. 58ECh. 5.1 - Prob. 59ECh. 5.1 - Prob. 60ECh. 5.1 - Prob. 61ECh. 5.1 - Prob. 62ECh. 5.1 - Prob. 63ECh. 5.1 - 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Simple Harmonic Motion - An introduction : ExamSolutions Maths Revision; Author: ExamSolutions;https://www.youtube.com/watch?v=tH2vldyP5OE;License: Standard YouTube License, CC-BY