(a) Explanation Given: d = − 2 cos ( π t ) The equation of simple harmonic motion is given by, y = a cos ω t And the given equation is, d = − 2 cos ( π t ) Therefore, the motion of the object is simple harmonic motion. (b) To determine To find: The maximum displacement. Explanation Given: d = − 2 cos ( π t ) The equation of simple harmonic motion is given by, y = a cos ω t And the given equation is, d = − 2 cos ( π t ) The amplitude is, | a | = | − 2 | = 2 Therefore, the maximum displacement is 2 . (c) To determine To find: The time required for one oscillation. Explanation Given: d = − 2 cos ( π t ) The equation of simple harmonic motion is given by, y = a cos ω t And the given equation is, d = − 2 cos ( π t ) The time period, T = 2 π ω = 2 π π = 2 The time required for one oscillation is 2 . (d) To determine To find: The time required for one oscillation. Explanation Given: d = − 2 cos ( π t ) The equation of simple harmonic motion is given by, y = a cos ω t And the given equation is, d = − 2 cos ( π t ) The frequency is calculated as, f = 1 T = 1 2 Therefore, the frequency is 1 2 .

9th Edition

ISBN: 9780321716835

Author: Michael Sullivan

Publisher: Addison Wesley

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Question

Chapter 8, Problem 67RE

(a)

To determine

To describe:The motion of the object.

(a)

Expert Solution

Explanation of Solution

Given: $d=−2cos(πt)$

The equation of simple harmonic motion is given by,

$y=acosωt$

And the given equation is,

$d=−2cos(πt)$

Therefore, the motion of the object is simple harmonic motion.

(b)

To determine

To find: The maximum displacement.

(b)

Expert Solution

Explanation of Solution

Given: $d=−2cos(πt)$

The equation of simple harmonic motion is given by,

$y=acosωt$

And the given equation is,

$d=−2cos(πt)$

The amplitude is,

$|a|=|−2|=2$

Therefore, the maximum displacement is $2$ .

(c)

To determine

To find: The time required for one oscillation.

(c)

Expert Solution

Explanation of Solution

Given: $d=−2cos(πt)$

The equation of simple harmonic motion is given by,

$y=acosωt$

And the given equation is,

$d=−2cos(πt)$

The time period,

$T=2πω=2ππ=2$

The time required for one oscillation is $2$ .

(d)

To determine

To find: The time required for one oscillation.

(d)

Expert Solution

Explanation of Solution

Given: $d=−2cos(πt)$

The equation of simple harmonic motion is given by,

$y=acosωt$

And the given equation is,

$d=−2cos(πt)$

The frequency is calculated as,

$f=1T=12$

Therefore, the frequency is $12$ .

Chapter 8, Problem 66RE

Chapter 8, Problem 68RE

Chapter 8 Solutions

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