Mechanical Properties of Fluids

Question

The kinetic energy of particle executing simple harmonic motion is 6J at mean position and 4J at a distance 4 cm from the mean position. What is the amplitude of oscillation of particle?

Solution

Let the particle of mass m vibrate with frequency $straight omega$ and A be the amplitude of oscillation.
The kinetic energy of particle at a distance y from mean position is,
$space space space space space space space space space space space space space space space straight K. straight E space equals space 1 half mω squared open parentheses straight A squared minus straight y squared close parentheses space Here comma space straight K. straight E space at space mean space position space is space 6 space straight J. space 6 space equals space 1 half mω squared space left parenthesis straight A squared space minus 0 squared right parenthesis space equals space 1 half mω squared straight A squared space space space space space space space... space left parenthesis 1 right parenthesis thin space straight K. straight E space at space straight a space distance space 4 space cm space from space mean space position space is space 4 straight J 4 space equals space 1 half mω squared space left square bracket straight A squared space minus space left parenthesis 0.04 right parenthesis squared right square bracket 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 left parenthesis 2 right parenthesis thin space Dividing space left parenthesis 1 right parenthesis space by space left parenthesis 2 right parenthesis comma space we space get space space space space space space fraction numerator 6 over denominator space 4 end fraction space equals space fraction numerator straight A squared over denominator straight A squared minus left parenthesis 0.04 right parenthesis squared end fraction space rightwards double arrow space space 6 left square bracket straight A squared space minus space left parenthesis 0.04 right parenthesis squared right square bracket space equals space 4 straight A squared space rightwards double arrow space space straight A squared space equals space 3 space left parenthesis 0.04 right parenthesis squared space rightwards double arrow space straight A space equals space 0.04 space square root of 3 space straight m space equals space 4 square root of 3 space cm$

A is the amplitude of the oscillation.

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Mechanical Properties Of Fluids

The kinetic energy of particle executing simple harmonic motion is 6J at mean position and 4J at a distance 4 cm from the mean position. What is the amplitude of oscillation of particle?

Some More Questions From Mechanical Properties of Fluids Chapter

What is an oscillatory motion?

What is time period?

Define frequency.

What is the condition for motion to be simple harmonic motion?

In the displacement equation y = r sin(ωt/ + ϕ) what does ϕ called and what information does it give?

What determines the natural frequency of an oscillator?

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.

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