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NEET PHYSICSOscillationsEasy

Question

The phase difference between displacement and acceleration of a particle in a simple harmonic motion is:

A

\frac{3\pi}{2} \text{ rad}

B

\frac{\pi}{2} \text{ rad}

C

zero

D

\pi \text{ rad}

Step-by-Step Solution

  1. Displacement Equation: Let the displacement of a particle executing Simple Harmonic Motion (SHM) be given by: x=Asin⁡(ωt)x = A \sin(\omega t) where AA is the amplitude and ω\omega is the angular frequency.
  2. Velocity Equation: Velocity vv is the time derivative of displacement: v=dxdt=Aωcos⁡(ωt)=Aωsin⁡(ωt+π2)v = \frac{dx}{dt} = A\omega \cos(\omega t) = A\omega \sin(\omega t + \frac{\pi}{2}) (Phase difference between displacement and velocity is π/2\pi/2).
  3. Acceleration Equation: Acceleration aa is the time derivative of velocity: a=dvdt=ddt[Aωcos⁡(ωt)]=−Aω2sin⁡(ωt)a = \frac{dv}{dt} = \frac{d}{dt}[A\omega \cos(\omega t)] = -A\omega^2 \sin(\omega t) Using the trigonometric identity −sin⁡θ=sin⁡(θ+π)-\sin \theta = \sin(\theta + \pi), we can write: a=Aω2sin⁡(ωt+π)a = A\omega^2 \sin(\omega t + \pi)
  4. Phase Difference: Comparing the phase of displacement (ωt)(\omega t) and acceleration (ωt+π)(\omega t + \pi), the difference is: Δϕ=(ωt+π)−(ωt)=π rad\Delta \phi = (\omega t + \pi) - (\omega t) = \pi \text{ rad}
  5. Conclusion: The acceleration is always in opposite phase (180∘180^\circ or π\pi radians) to the displacement .

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from Oscillations. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSOscillationsdifferencebetweendisplacementaccelerationparticle

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