First slide

Simple harmonic 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 $3 .92 \times 10^{- 3} m$ . What must be the least period of these oscillations, so that the object is not detached from the platform

Moderate

A

0.1256 sec
B

0.1356 sec
C

0.1456 sec
D

0.1556 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 $\Rightarrow mg = {maω}^{2}$
$\Rightarrow ω = \sqrt{g / a} = \sqrt{\frac{9 .8}{3 .92 \times 10^{- 3}}} = 50$
$\Rightarrow T = \frac{2 π}{ω} = \frac{2 π}{50} = 0 .1256 \sec$

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