Question 266: Oscillations

Question

A horizontal platform with a small object placed on it executes a linear S.H.M. in the vertical direction. The amplitude of oscillation is 40 cm . What should be the least period of these oscillations, so that the object is not detached from the platform? [Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$]

Accepted Answer

From the diagram,
$$\mathrm{mg}-\mathrm{N}=\mathrm{ma}$$
For the object to just lose the Contact with the surface,
$\mathrm{N}=0$
$$\begin{array}{ll}
	herefore & m g=m a \
	herefore & g=a \
	herefore & g=A \omega^2
\end{array}$$
$$\begin{aligned}
& 	herefore \quad \omega=\sqrt{\frac{g}{A}}=\sqrt{\frac{10}{0.4}}=\sqrt{\frac{100}{4}}=\frac{10}{2}=5 \
& 	herefore \quad \frac{2 \pi}{T}=5 \
& 	herefore \quad T=\frac{2 \pi}{5}=0.4 \pi
\end{aligned}$$

Answer

$0.2 \pi \mathrm{~s}$

Answer

$0.3 \pi \mathrm{~s}$

Answer

$0.4 \pi \mathrm{~s}$

Answer

$0.5 \pi \mathrm{~s}$

Oscillations

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