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JEE Main 2014 (9 Apr, Shift 1) · Damped, Forced Oscillations & Superposition

Damped, Forced Oscillations & Superposition question from JEE Main 2014 (9 Apr, Shift 1)

Q18JEE Main 2014 · 9 APR · SHIFT 1Medium

Damped, Forced Oscillations & Superposition

A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; x = a1 cos $\omega$ t and y = a2 cos 2 $\omega$ t traces a curve given by:

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Answer: (a)

$y = a_2\cos 2\omega t = a_2(2\cos^2\omega t - 1)$ and $\cos\omega t = x/a_1$ .
$y = a_2\left(\frac{2x^2}{a_1^2} - 1\right)$ : a parabola opening upward.
Vertex at $(0, -a_2)$ ; at $x = \pm a_1$ , $y = +a_2$ .
So the answer is (a).

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