The displacement of a particle executing simple harmonic motion is represented by = r sin ωt. Find the velocity and acceleration of the particle in terms of displacement.

Solution

Displacement of particle executing S.H.M is given by,
y= $space space r space sinωt$
Velocity of the particle is,

$straight v equals dy over dt equals straight d over dt left parenthesis straight r space sin space ωt right parenthesis space equals space rω space cos space ωt$
This implies,
$straight v space equals space straight omega space square root of straight r squared cos squared ωt end root space space space equals space straight omega space square root of straight r squared left parenthesis 1 minus sin squared ωt right parenthesis end root space space equals space straight omega space square root of straight r squared minus straight r squared sin squared ωt end root space straight v space equals space straight omega square root of straight r squared minus straight y squared end root space And comma space Acceleration comma space straight a space space equals space dv over dt space equals space straight d over dt open parentheses rω space cos space ωt close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space minus space rω squared space sin space ωt space equals space minus straight omega squared straight y space That space is comma space straight a space equals space minus straight omega squared straight y$

Some More Questions From Mechanical Properties of Fluids Chapter

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Mechanical Properties Of Fluids

The displacement of a particle executing simple harmonic motion is represented by = r sin ωt. Find the velocity and acceleration of the particle in terms of displacement.

Some More Questions From Mechanical Properties of Fluids Chapter

What is periodic motion?

Write down the expression for the instantaneous velocity and acceleration of particle vibrating in simple harmonic motion.

How do you define the mean position of particle executing simple harmonic motion?

Define amplitude.

What is the net displacement of the particle executing simple harmonic motion in one complete oscillation?

Are all the periodic motions simple harmonic?

Does the time period of particle vibrating in simple harmonic motion depend upon its displacement?

Where will the particle executing simple harmonic motion have acceleration maximum and speed zero?

What is the average velocity of the particle executing simple harmonic motion over one complete oscillation?

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