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Question

Two identical springs of spring constant k each are connecetd 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
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B
2:1
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C
4:1
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D
1:4
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Solution

The correct option is A 1:2
Case I : Two springs of equal spring constant are in series arrangement.
effective spring constant (KS)=K×K2K=K2
frequency  of oscillation (ns)=12πKSm=12πK2m     ...(1)
Case II : Two springs of equal spring constant are in parallel arrangement.
effective spring constant (KP)=2K
Frequency of oscillation (nP)=12πKPm
=12π2Km     ...(2)
From (1) & (2) we get
nSnP=12πKSm12πKPm=12

Physics

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