Question 228: Oscillations

Question

The ratio of the frequencies of two simple pendulums is $4: 3$ at the same place. The ratio of their respective lengths is

Accepted Answer

$$ \begin{aligned} &	ext { Period of simple pendulum, }\ &\begin{array}{ll}  & \mathrm{T}=2 \pi \sqrt{\frac{L}{g}} \ & \mathrm{f}=\frac{1}{\mathrm{~T}}=\frac{1}{2 \pi} \sqrt{\frac{g}{L}} \ \Rightarrow & \mathrm{f} \propto \frac{1}{\sqrt{L}} \	herefore  & \frac{\mathrm{f}_1}{\mathrm{f}_2}=\sqrt{\frac{\mathrm{L}_2}{\mathrm{~L}_1}} \ 	herefore & \frac{\mathrm{~L}_2}{\mathrm{~L}_1}=\left(\frac{\mathrm{f}_1}{\mathrm{f}_2}ight)^2=\left(\frac{4}{3}ight)^2=\frac{16}{9} \ 	herefore & \frac{\mathrm{~L}_1}{\mathrm{~L}_2}=\frac{9}{16} \end{array} \end{aligned} $$

Answer

$3: 4$

Answer

$4: 3$

Answer

$9: 16$

Answer

$16: 9$

Oscillations

The ratio of the frequencies of two simple pendulums is 4: 3 at the same place. The ratio of their respective lengths is

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