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JEE Main 202117 MarchMorning Shift
Exam
JEE Main
Year
2021
Date
17 March
Shift
Morning Shift
Subject
Physics
Chapter
Oscillations

JEE Main 2021 · 17 March · Morning Shift · Physics · Oscillations

For what value of displacement the kinetic energy and potential...

For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?

Options

  1. Ax=0x = 0
  2. Bx=±Ax = \pm A
  3. Cx=±A2x = \pm \dfrac{A}{\sqrt{2}}
  4. Dx=A2x = \dfrac{A}{2}

Correct answer

C. x=±A2x = \pm \dfrac{A}{\sqrt{2}}

Step-by-step solution

KE=PEKE = PE

12mω2(A2−x2)=12mω2x2\dfrac{1}{2}m{\omega}^{2}\left({A}^{2} - {x}^{2}\right) = \dfrac{1}{2}m{\omega}^{2}{x}^{2}

A2−x2=x2{A}^{2} - {x}^{2} = {x}^{2}

2x2=A22{x}^{2} = {A}^{2}

x=±A2x = \pm \dfrac{A}{\sqrt{2}}

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