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Question

Two springs of force constants k1 and k2 are connected as shown figure. The time period of vertical oscillations of mass m is given by


A
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B
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C
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D
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Solution

The correct option is A
The two springs are connected in parallel. Therefore, the force constant of the combination is
K=k1+k2
This can be shown as follows: Let x be the extension in each spring. Since the total force is mg,
we get, mg=(k1+k2)x=kx. Thus k=k1+k2. Therefore
T=2πmk=2πm(k1+k2)
Hence the correct choice is (a).

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