Some springs are combined in series and parallel arrangement as shown in the figure and a mass m is suspended from them. The ratio of their frequencies will be
A
1:1
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B
2:1
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C
√3:2
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D
4:1
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Solution
The correct option is C√3:2 Case I :
Both springs are in series, ∴ effective spring constant (Ks)1=K1K2K1+K2=K2
Frequency of oscillation (fs)1=12π√Ksm =12π√K2m...(1)
Case II :
Two springs are in parallel combination, which is in series arrangement with other spring.
Effective spring constant (Ks)2=(2K)(K)3K=2K3
Frequency of oscillation (fs)2=12π√(Ks)2m =12π√2K3m...(2)
From (1) & (2) (fs)1(fs)2=√32