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JEE Main 20149 AprilOnline
Exam
JEE Main
Year
2014
Date
9 April
Mode
Online
Subject
Physics
Chapter
Oscillations

JEE Main 2014 · 9 April · Online · Physics · Oscillations

A particle which is simultaneously subjected to two perpendicular...

A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; x=a1cos\omegatx = {a}_{1}cos \omegat and y=a2cos⁡2\omegaty = {a}_{2}\cos 2\omegat traces a curve given by :A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; x = a _ 1 cosA particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; x = a _ 1 cosA particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; x = a _ 1 cosA particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; x = a _ 1 cos

Options

  1. AIdentify and name the compounds given below respectively.
  2. BIdentify and name the compounds given below respectively.
  3. CIdentify and name the compounds given below respectively.
  4. DIdentify and name the compounds given below respectively.

Correct answer

D. Identify and name the compounds given below respectively.

Step-by-step solution

x=a1cos\omegatx = {a}_{1}cos \omegat

y=a2cos⁡(2\omegat)y = {a}_{2}\cos \left(2\omegat\right)

=a2{2cos⁡2\omegat−1}= {a}_{2}\left\{2\cos^{2} \omegat - 1\right\}

=a2{2(xa1)2−1}= {a}_{2}\left\{2{\left(\dfrac{x}{{a}_{1}}\right)}^{2} - 1\right\}

∴ya2=2x2a12−1∴ \dfrac{y}{{a}_{2}} = \dfrac{2{x}^{2}}{{a}_{1}^{2}} - 1

∴a12y=2a2x2−a12a2∴ {a}_{1}^{2}y = 2{a}_{2}{x}^{2} - {a}_{1}^{2}{a}_{2}

which is a parabola symmetrical about y-axis opening in upward direction
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