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Questions  

A particle is executing SHM according to the equation x=Acosωt. Average speed of the particle during the interval 0tπ6ω.

a
3Aω2
b
3Aω4
c
3Aωπ
d
3Aωπ(2−3)

detailed solution

Correct option is D

Average velocity v¯=∫0t dxdt⋅dtt=∫0t dxt=x(t)−x(0)t=A(cos⁡π/6−1)π/6ω=3Aωπ(3−2)Since particle does not change its direction in the given interval, average speed becomes |v¯|=3Aωπ(2−3)

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A horizontal platform with an object placed on it is executing S.H.M. in the vertical direction. The amplitude of oscillation is 3.92×103m . What must be the least period of these oscillations, so that the object is not detached from the platform 


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