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JEE Main 202127 JulyMorning Shift
Exam
JEE Main
Year
2021
Date
27 July
Shift
Morning Shift
Subject
Physics
Chapter
Oscillations

JEE Main 2021 · 27 July · Morning Shift · Physics · Oscillations

A particle starts executing simple harmonic motion ( SHM ) of...

A particle starts executing simple harmonic motion (SHM)( SHM ) of amplitude aa and total energy E.E . At any instant, its kinetic energy is 3E4\dfrac{3E}{4}, then its displacement yy is given by:

Options

  1. Ay=ay = a
  2. By=a2y = \dfrac{a}{\sqrt{2}}
  3. Cy=a32y = \dfrac{a\sqrt{3}}{2}
  4. Dy=a2y = \dfrac{a}{2}

Correct answer

D. y=a2y = \dfrac{a}{2}

Step-by-step solution

E=12Ka2E = \dfrac{1}{2}K{a}^{2}
3E4=12K(a2−y2)v\dfrac{3E}{4} = \dfrac{1}{2}K\left({a}^{2} - {y}^{2}\right)v
34×12Ka2=12K(a2−y2)\dfrac{3}{4} \times \dfrac{1}{2}K{a}^{2} = \dfrac{1}{2}K\left({a}^{2} - {y}^{2}\right)
y2=a2−3a24{y}^{2} = {a}^{2} - \dfrac{3{a}^{2}}{4}
y=a2y = \dfrac{a}{2}
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