Question 298: Oscillations

Question

Three masses $500 \mathrm{~g}, 300 \mathrm{~g}$ and 100 g are suspended at the end of spring as shown in figure and are in equilibrium. When the 500 g mass is removed, the system oscillates with a period of 3 second. When the 300 g mass is also removed it will oscillate with a period of

Accepted Answer

We know $\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{~m}}{\mathrm{k}}}$
When 500 g is removed, $\mathrm{m}=(100+300) \mathrm{g}$
$$=0.4 \mathrm{~kg}$$
$$\begin{aligned}
	herefore \quad & \mathrm{T}=2 \pi \sqrt{\frac{0.4}{\mathrm{k}}}=3 \mathrm{~s} \
& \frac{2 \pi}{\sqrt{\mathrm{k}}}=\frac{3}{\sqrt{0.4}}\quad	ext{... (i)}
\end{aligned}$$
Similarly when 300 g is removed,
$\mathrm{m}^{\prime}=100 \mathrm{~g}=0.1 \mathrm{~kg}$
$\mathrm{T}^{\prime}=2 \pi \sqrt{\frac{0.1}{\mathrm{k}}}=\mathrm{x}$
$$\begin{array}{ll}
	herefore & \frac{2 \pi}{\sqrt{\mathrm{k}}}=\frac{\mathrm{x}}{\sqrt{0.1}} \
& \frac{3}{\sqrt{0.4}}=\frac{\mathrm{x}}{\sqrt{0.1}} \quad	ext{.... (from (i))}\
	herefore \quad & x=\mathrm{T}^{\prime}=\frac{3}{2}=1.5 \mathrm{~s}
\end{array}$$

Answer

1 s

Answer

1.5 s

Answer

2 s

Answer

2.5 s

Oscillations

Three masses 500 \mathrm{~g}, 300 \mathrm{~g} and 100 g are suspended at the end of spring as shown in figure and are in equilibrium. When the 500 g mass is removed, the system oscillates with a period of 3 second. When the 300 g mass is also removed it will oscillate with a period of

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