A horizontal platform with an object placed on it is executing S.H.M. in the vertical direction. The amplitude of oscillation is $$4.0$$ x $$10-3$$ m. What must be the least period of these oscillations, so that the object is not detached from the platform? (Take$$ g $$=$$ $$10$$ $$m/s2)

Question

A horizontal platform with an object placed on it is executing S.H.M. in the vertical direction. The amplitude of oscillation is $$4.0$$ x $$10-3$$ m. What must be the least period of these oscillations, so that the object is not detached from the platform? (Take$$ g $$=$$ $$10$$ $$m/s2)

Infinity Learn · Accepted Answer

By drawing free body diagram of object during the downward motion at extreme position, for equilibrium of massmg $$-$$ R $$=$$ mA $$(A$$ $$=$$ $$Acceleration)For$$ critical condition R $$=$$ $$0so$$ mg $$=$$ mA ⇒ mg $$=$$ mαω$$2$$  ⇒ω $$=$$ ga $$=$$ $$104.0$$×$$10-3$$ $$=$$ $$50$$⇒T $$=$$ $$2$$πω $$=$$ $$2$$$$π$$$$50$$ $$=$$ π$$25sec$$

A horizontal platform with an object placed on it is executing S.H.M. in the vertical direction. The amplitude of oscillation is 4.0 x $10^{- 3}$ m. What must be the least period of these oscillations, so that the object is not detached from the platform? (Take g = 10 $m / s^{2}$ )

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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 4.0 x 10-3 m. What must be the least period of these oscillations, so that the object is not detached from the platform? (Take g = 10 m/s2)

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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 4.0 x $10^{- 3}$ m. What must be the least period of these oscillations, so that the object is not detached from the platform? (Take g = 10 $m / s^{2}$ )