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  •  A  particle which is simultaneously subjected to two perpendicular Simple Harmonic  Motions represented by  ;         </p

 A  particle which is simultaneously subjected to two perpendicular Simple Harmonic  Motions represented by  ;         

x= a_{1}\: \cos \omega\: t\: \: and \: \: y=a_{2}\cos 2\omega t

traces a curve given by :

Option: 1


Option: 2


Option: 3


Option: 4


Answers (1)

best_answer

Given,

y=a_2 \cos 2 \omega t=a_2\left(2 \cos ^2 \omega t-1\right)
Now, from the equation along x-axis,

 \cos \omega t=\frac{x}{a_1}
Substituting this value back,

 y=a_2\left(2 \times\left(\frac{x}{a_1}\right)^2-1\right)
Hence, this describes a parabola facing upwards.

Posted by

HARSH KANKARIA

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