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Physics · Simple Harmonic Motion

NEET (UG) 2023 — Question 47

The x−tx-t graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at t=2 st=2 \mathrm{~s} is :

Question figure
  1. Option A:

    −π28 m s−2-\frac{\pi^{2}}{8} \mathrm{~m} \mathrm{~s}^{-2}

  2. Option B:

    π216 m s−2\frac{\pi^{2}}{16} \mathrm{~m} \mathrm{~s}^{-2}

  3. Option C:

    −π216 m s−2-\frac{\pi^{2}}{16} \mathrm{~m} \mathrm{~s}^{-2}

    Correct
  4. Option D:

    π28 m s−2\frac{\pi^{2}}{8} \mathrm{~m} \mathrm{~s}^{-2}

Answer: C

Step-by-step solution

Position of particle as function of time x=Asin⁡ωtx=A \sin \omega t

From figure,

A=1ω=2π8x=sin⁡π4tv=dxdtv=π4cos⁡π4ta=dvdta=−π216sin⁡π4t at t=2 sa=−π216 m/s2\begin{aligned} & A=1 \\ & \omega=\frac{2 \pi}{8} \\ & x=\sin \frac{\pi}{4} t \\ & v=\frac{d x}{d t} \\ & v=\frac{\pi}{4} \cos \frac{\pi}{4} t \\ & a=\frac{d v}{d t} \\ & a=-\frac{\pi^2}{16} \sin \frac{\pi}{4} t \\ & \text { at } t=2 \mathrm{~s} \\ & a=-\frac{\pi^2}{16} \mathrm{~m} / \mathrm{s}^2 \end{aligned}
Solution figure

Answer key and solution verified before publishing.

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Exam
NEET (UG) 2023
Paper
2023 paper
Subject
Physics
Chapter
Simple Harmonic Motion
Topic
Kinematics of SHM, Phase and Energy in SHM
The x-t graph of a particle performing simple harmonic motion is… | NEET (UG) 2023 PYQ with Solution · DhiX AI