A horizontal platform with an object placed on it is executing S H M in the vertical direction. The amplitude of oscillation is 2.5 c m . What must be the least period of these oscillations so that th

Question

A horizontal platform with an object placed on it is executing S H M in the vertical direction. The amplitude of oscillation is 2.5 c m . What must be the least period of these oscillations so that the object is not detached? (Given : g = 10 m s - 2 )

TestHub · Accepted Answer

At the extreme location, the forces on the object are mg and mω²A in opposite directions

For an object to always be in contact will platform

$m ω^{2} A \leq m g$

or $ω = \sqrt{\frac{g}{A}}$ or $\frac{T}{2 π} = \sqrt{\frac{A}{g}}$
or $T = 2 π \sqrt{\frac{A}{g}} = 2 π \sqrt{\frac{2.5}{1000}} = \frac{π}{10} s$

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