Show that if acceleration of particle at extreme position is twice the magnitude of velocity at mean position, then time period of oscillation of particle is πs.

Solution

Let A be the amplitude and $straight omega$ be the frequency of oscillation.
Therefore,
$straight v subscript straight o space equals space Aω space and space straight a subscript straight o space equals space Aω squared space So comma space straight a subscript straight o over straight v subscript straight o space equals space Aω squared over Aω space equals space straight omega space straight i. straight e. comma space fraction numerator 2 straight pi over denominator straight T end fraction space equals space straight a subscript straight o over straight v subscript straight o space rightwards double arrow space straight T space equals space 2 straight pi space straight v subscript straight o over straight a subscript straight o space Here comma space we space have space straight a subscript straight o space equals space 2 space straight v subscript straight o space Therefore comma space Time space period space of space the space oscillation space of space particle space is comma space straight T space equals space πs$

Some More Questions From Mechanical Properties of Fluids Chapter

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Mechanical Properties Of Fluids

Show that if acceleration of particle at extreme position is twice the magnitude of velocity at mean position, then time period of oscillation of particle is πs.

Some More Questions From Mechanical Properties of Fluids Chapter

Is there any relation between uniform circular motion and simple harmonic motion?

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?

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