Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

The displacement d (in meters) of an object at time t (in seconds) is given $d = 6 \cos (π t)$
(a) Describe the motion of the object.
(b) What is the maximum displacement from its resting position?
(c) What is the time required for one oscillation?
(d) What is the frequency?

a) It is a simple harmonic motion

b) The amplitude is 6

c) The period is 2

d) The frequency is $\frac{1}{π}$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

Our given equation is $d = 6 \cos (π t)$

Part (a) Step 1: Explanation

As the object is modeled by cosine function the given wave is simple harmonic.

Part (b) Step 1: The maximum displacement of object from resting position is the amplitude

Comparing the equation with standard wave equation we get $a = 6$

Part (c) Step 1: Find period

We get,

$ω = \frac{2 π}{T} π = \frac{2 π}{T} T = 2$

Part (d) Step 1: Find the frequency

We get,

$f = \frac{1}{ω} f = \frac{1}{π}$

Step 6: Conclusion

a) It is a simple harmonic motion

b) The amplitude is 6

c) The period is $2$

d) The frequency is $\frac{1}{π}$

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Precalculus Enhanced with Graphing Utilities

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Short Answer

The displacement d (in meters) of an object at time t (in seconds) is given $d = 6 \cos (π t)$
(a) Describe the motion of the object.
(b) What is the maximum displacement from its resting position?
(c) What is the time required for one oscillation?
(d) What is the frequency?

Step by Step Solution

Step 1: Given information

Part (a) Step 1: Explanation

Part (b) Step 1: The maximum displacement of object from resting position is the amplitude

Part (c) Step 1: Find period

Part (d) Step 1: Find the frequency

Step 6: Conclusion

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Precalculus Enhanced with Graphing Utilities

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Short Answer

The displacement d (in meters) of an object at time t (in seconds) is given d=6cos(πt)(a) Describe the motion of the object.(b) What is the maximum displacement from its resting position?(c) What is the time required for one oscillation?(d) What is the frequency?

Step by Step Solution

Step 1: Given information

Part (a) Step 1: Explanation

Part (b) Step 1: The maximum displacement of object from resting position is the amplitude

Part (c) Step 1: Find period

Part (d) Step 1: Find the frequency

Step 6: Conclusion

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The displacement d (in meters) of an object at time t (in seconds) is given $d = 6 \cos (π t)$
(a) Describe the motion of the object.
(b) What is the maximum displacement from its resting position?
(c) What is the time required for one oscillation?
(d) What is the frequency?