Question

Two identical springs of spring constant $k$ each are connected in series and parallel as shown in figure. A mass $M$ is suspended from them. The ratio of their frequencies of vertical oscillation will be

• A. $1:2$
• B. $3:1$
• C. $4:1$
• D. $1:4$

Answer 1

The correct option is A $1:2$

In first case two springs are in series, hence effective resistance is $k_s=\frac{k\times k}{k+k}=\frac{k}{2}$
In second case two springs are in parallel, hence effective resistance is
$k_p=k+k=2k$
Ratio of frequencies in these two cases is
$\therefore \frac{n_s}{n_p}=\frac{\frac{1}{2\pi }\sqrt{\frac{k_s}{M}}}{\frac{1}{2\pi }\sqrt{\frac{k_p}{M}}}=\sqrt{\frac{k_s}{k_p}}=\sqrt{\frac{k/2}{2k}}=\frac{1}{2}$.