Question

# In the fig. $$S1$$ and $$S2$$ are identical springs. The oscillation frequency of mass $$m$$ is $$f$$. If one spring is removed, the frequency will become

A
f
B
f×2
C
f×2
D
f/2

Solution

## The correct options are C $$f\times\sqrt{2}$$ D $$f/\sqrt{2}$$For the given figure $$f=\dfrac{1}{2\pi}\sqrt{\dfrac{k_{eq}}{m}}=\dfrac{1}{2\pi}\sqrt{\dfrac{2k}{m}}$$    .....(i)If one spring is removed, then $$k_{eq}=k$$ and $$f'=\dfrac{1}{2\pi}\sqrt{\dfrac km}$$   .....(ii)From equation (i) and (ii), $$\dfrac{f}{f'}=\sqrt 2\Rightarrow f'=\dfrac{f}{\sqrt 2}$$Physics

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