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use the information to calculate the periodic time of the point

use the information to calculate the periodic time of the point

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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use the information to calculate the periodic time of the point

stion 2 A point in a machine moves with simple harmonic motion. When this point is 0.8 metre from the mid path, its velocity is 10 m/s and when 1.5 metres from the centre of its path its velocity is 4 m/s. Calculate:
Transcribed Image Text:stion 2 A point in a machine moves with simple harmonic motion. When this point is 0.8 metre from the mid path, its velocity is 10 m/s and when 1.5 metres from the centre of its path its velocity is 4 m/s. Calculate:
Expert Solution
Step 1

Write the formula for the velocity of the point in simple harmonic motion in terms of amplitude and angular velocity.

v1=ωA2-x12

Here, v1 is the velocity of the point at a distance x1 from the mean position, A is the amplitude of oscillation, and ω is the angular velocity of motion.

Substitute 10 m/s for v1, and 0.8 m for x1.

10 m/s=ωA2-0.8 m2               ... (1)

Write the formula for the velocity of the point in simple harmonic motion.

v2=ωA2-x22

Here, v2 is the velocity of the point at a distance x2 from the mean position.

Substitute 4 m/s for v2, and 1.5 m for x2.

4 m/s=ωA2-1.5 m2               ... (2)

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