Question

The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is

• A. $0.5 \pi$
• B. $\pi$
• C. $0.707 \pi$
• D. zero

Answer 1

The Correct Option is A

The displacement equation of the particle executing SHM is  

Acceleration = Aω²sin ωt

the instantaneous velocity and acceleration have a 0.5π phase difference.

Discover More From This Chapter: Simple Harmonic Motion

Answer 2

The Correct Answer is (A)

Real Life Applications

• It is used in the design of shock absorbers and suspension systems in cars.
• It is also used in the design of loudspeakers and other devices that produce sound waves.

Question can also be asked as

• What are the defining characteristics of simple harmonic motion?
• Define instantaneous velocity in the context of simple harmonic motion.
• What is phase difference in the context of simple harmonic motion?
• What is the phase difference between the velocity and acceleration of a particle executing simple harmonic motion?
• How particle in SHM vary wit time?

Answer 3

The Correct Answer is (A)

• Let the word X represent the particle's displacement in relation to the point around which it is performing simple harmonic motion.
• Consequently, if the particle's initial phase is θ  and angular velocity, the particle's displacement equation might then be constructed.
• X=Asin(ωt+θ), A is the amplitude which is the largest displacement with respect to the simple harmonic motion's execution point.

⇒dX/dt=d[Asin(ωt+θ)] / dt

⇒v=Aωcos(ωt+θ)

⇒Aωcos(ωt+θ)=−Aωsin(ωt+θ+π/2)
∴v=−Aωsin(ωt+θ+π/2)

the phase difference between displacement and velocity as π/2. As a result, the phase difference between velocity and displacement for a particle performing simple harmonic motion is equal to π/2 radian.

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Related Topics
Simple Harmonic Motion	Wave Function	Simple Harmonics