Question

Identical springs of spring constant $K$ are connected in series and parallel combinations. A mass $m$ is suspended from them. The ratio of their frequencies of vertical oscillations will be

• A. 1:4
• B. 1:2
• C. 4:1
• D. 2:1

Answer 1

The correct option is A 1:4

From Formula 1. in series combination, ,
$k_{eq}=\frac{K\times K}{K+K}=\frac{K}{2}$.
$\therefore f_1=\frac{1}{2\pi }\sqrt{\frac{K}{2m}}$ ...(1)
For parallel combination, $k_{eq}=2K$
$\therefore f_2=\frac{1}{2\pi }\sqrt{\frac{2K}{m}}$...(2)
Taking ratio, we get answer as$1:4$ Option A is correct.