Question 305: Oscillations

Question

Two identical springs of constant '$$\mathrm{K}$$' are connected in series and parallel in shown in figure. A mass '$$\mathrm{M}$$' is suspended from them. The ratio of their frequencies is series to parallel combination will be

Accepted Answer

In series combination, the effective spring constant
$$\mathrm{k}_1=\frac{\mathrm{k}}{2}$$
In the parallel combination, the effective spring constant is
$$\begin{aligned}
k_2 & =2 k \
f_1 & =\frac{1}{2 \pi} \sqrt{\frac{k_1}{m}}=\frac{1}{2 \pi} \sqrt{\frac{k}{2 m}} \
f_2 & =\frac{1}{2 \pi} \sqrt{\frac{k_2}{m}}=\frac{1}{2 \pi} \sqrt{\frac{2 k}{m}} \
	herefore \frac{f_1}{f_2} & =\sqrt{\frac{1}{4}}=\frac{1}{2}
\end{aligned}$$

Answer

$$1: 2$$

Answer

$$1: 4$$

Answer

$$4: 1$$

Answer

$$1: \sqrt{2}$$

Oscillations

Two identical springs of constant '$\mathrm{K}' are connected in series and parallel in shown in figure. A mass '\mathrm{M}$' is suspended from them. The ratio of their frequencies is series to parallel combination will be

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