Question 320: Oscillations

Question

A spring has a certain mass suspended from it and its period for vertical oscillations is '$$T_1$$'. The spring is now cut in to two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillations is now '$$\mathrm{T}_2$$'. The ratio $$\mathrm{T}_1 / \mathrm{T}_2$$ is

Accepted Answer

$$\mathrm{T}_1=2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}} .$$
Also, spring constant $$(\mathrm{k}) \propto \frac{1}{	ext { Length }(l)}$$
When the spring is half in length, then $$k$$ becomes twice.
$$\begin{array}{ll}
	herefore & \mathrm{T}_2=2 \pi \sqrt{\frac{\mathrm{m}}{2 \mathrm{k}}} \
	herefore & \frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{1}{\frac{1}{\sqrt{2}}}=\sqrt{2}
\end{array}$$

Answer

2

Answer

$$\sqrt{2}$$

Answer

$$\frac{1}{\sqrt{2}}$$

Answer

$$\frac{1}{2}$$

Oscillations

A spring has a certain mass suspended from it and its period for vertical oscillations is '$T_1'. The spring is now cut in to two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillations is now '\mathrm{T}_2'. The ratio \mathrm{T}_1 / \mathrm{T}_2$ is

Choose the correct answer: