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PhysicsSHMMiscellaneousMedium2 minPYQ_2014

PhysicsMediumsingle choice

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 :

Options:

Answer:

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

Stream:JEESubject:PhysicsTopic:SHMSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2014

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