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Oscillations — Physics STD 11 Science — Question

Rajasthan 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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