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Oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsOscillations3 Marks
Question
A horizontal platform with an object placed on it is executing SHM in the vertical direction. The amplitude of oscillation is $2.5cm$. What must be the least period of these oscillations so that the object is not detached from the platform? Take $g = 10ms^{-2}$?
✓

Answer

The object will not detach from the platform, if the angular frequency $\omega$is such that, during the downward motion, the maximum acceleration equals the acceleration due to gravity, i.e.,$\omega^2_\text{max}\text{A}=\text{g}$
$\omega_\text{max}=\sqrt{\frac{\text{g}}{\text{A}}}$
$\text{T}_\text{min}=\frac{2\pi}{\omega_\text{max}}$
$=2\pi\sqrt{\frac{\text{A}}{\text{g}}}$
Now $\text{A}=2.5\text{cm}$$=2.5\times10^{-2}\text{m}$
$\text{g}=10\text{ms}^{-2}$
Substituting thesa values we get $\text{T}_\text{min}=\frac{\pi}{10}$

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