First slide

Simple hormonic motion

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 $m / s^{2}$ )

Moderate

A

$\frac{π}{25} \sec$
B

$\frac{π}{18} \sec$
C

$\frac{π}{14} \sec$
D

$\frac{π}{20} \sec$

Solution

By drawing free body diagram of object during the downward motion at extreme position, for equilibrium of mass
mg - R = mA (A = Acceleration)
For critical condition R = 0
so mg = mA $\Rightarrow$ mg = ${mαω}^{2}$

$\Rightarrow ω = \sqrt{\frac{g}{a}} = \sqrt{\frac{10}{4.0 \times 10^{- 3}}} = 50$
$\Rightarrow T = \frac{2 π}{ω} = \frac{2 π}{50} = \frac{π}{25} \sec$

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