Derive the differential equation of simple harmonic motion.

Solution

The acceleration of particle executing simple harmonic motion, a = – ω²y

We know that the acceleration is second derivative of displacement.
Therefore,
$space space space space space space space space space space space space space space straight a equals fraction numerator straight d squared straight y over denominator dt squared end fraction therefore space space space fraction numerator straight d squared straight y over denominator dt squared end fraction equals negative straight omega squared straight y space space space space space space fraction numerator straight d squared straight y over denominator dt squared end fraction plus straight omega squared straight y equals 0$
The above equation represent the differential equation of simple harmonic motion.

Some More Questions From Mechanical Properties of Fluids Chapter

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Mechanical Properties Of Fluids

Derive the differential equation of simple harmonic motion.

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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