Q81 / 90 · JEE Main 2014 (09 Apr Online) · Physics

A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; $x = a_{1} \cos ω t$ and $y = a_{2} \cos 2 ω t$ traces a curve given by :

A
B
C
Correct answer
D

Solution

x = a_{1} \cos ω t

y = a_{2} \cos (2 ω t)

= a_{2} \{2 \cos^{2} ω t - 1\}

= a_{2} \{2 {(\frac{x}{a_{1}})}^{2} - 1\}

∴ \frac{y}{a_{2}} = \frac{2 x^{2}}{a_{1}^{2}} - 1

∴ 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

Hence, the correct answer is option: 'D'.

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