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The motion of a particle varies with time according to the relation y=asinωt+acosωt, then

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a
The motion is oscillatory but not S.H.M.
b
The motion is S.H.M. with amplitude a
c
The motion is S.H.M. with amplitude a2
d
The motion is S.H.M. with amplitude 2a

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detailed solution

Correct option is C

resultant of two amplitudes of simple harmonic motion is ,  R=a2+b2+2abcosϕ here a, b are amplitudes , ∅ is phase difference between two given waves The given equation can be written as y=asinωt+asinωt+π2  Here ϕ=π2  R=a2+a2+2aacosπ2  R=a2+a2=a2


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