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

Solution

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

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