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Some springs are combined in series and ...

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`

B

`2:1`

C

`sqrt(3):2`

D

`4:1`

Text Solution

Verified by Experts

The correct Answer is:
C
(c) For series arrangement , `f_(s)=(1)/(2pi)sqrt((k_(s))/(m))=(1)/(2pi)sqrt((k)/(2m))" "(because k_(s)=(k_(1)k_(2))/(k_(1)+k_(2))=(k)/(2))`
For parallel and series arrangement,
`f_(p)=(1)/(2pi)sqrt((2k)/(3m))" "(because k_(p)=(2k k)/(2k+k)=(2k)/(3))`
`implies (f_(s))/(f_(p))=sqrt((k)/(2m))xxsqrt((3m)/(2k))=(sqrt(3))/(2)impliessqrt(3):2`
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