Question 300: Oscillations

Question

A light spring is suspended with mass $$m_1$$ at its lower end and its upper end fixed to a rigid support. The mass is pulled down a short distance and then released. The period of oscillation is $$T$$ second. When a mass $$m_2$$ is added to $$m_1$$ and the system is made to oscillate, the period is found to be $$\frac{3}{2} T$$. The ratio $$m_1: m_2$$ is

Accepted Answer

The time period is $$T \propto \sqrt{\mathrm{m}}$$
$$\begin{aligned}
& 	herefore \quad \frac{T}{\frac{3}{2}T}=\frac{\sqrt{m_1}}{\sqrt{m_1+m_2}} \
& 	herefore \quad \frac{2}{3}=\frac{\sqrt{m_1}}{\sqrt{m_1+m_2}} \
& 	herefore \quad \frac{4}{9}=\frac{m_1}{m_1+m_2} \
& 	herefore \quad 4 m_1+4 m_2=9 m_1 \
& 	herefore \quad 5 m_1=4 m_2 \
& 	herefore \quad \frac{m_1}{m_2}=\frac{4}{5}
\end{aligned}$$

Answer

$$2: 3$$

Answer

$$3: 4$$

Answer

$$4: 5$$

Answer

$$5: 6$$

Oscillations

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