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Question

A block of mass m is suspended by different springs of force constant shown in figure.
Let time period of oscillation in these four position be T1,T2,T3 and T4. Then,
(Consider springs to be massless.)

A
T1=T2=T4
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B
T1=T2 and T3=T4
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C
T1=T2=T3
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D
T1=T3 and T2=T4
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Solution

The correct option is B T1=T2 and T3=T4
Time period of oscillations for a spring block system is given by 2πmK
where K is the equivalent force constant of the spring system.
Here in first and second figure equivalent force constant is only K whereas in third and fourth figure springs are taken in parallel combination because in both springs deformations are always equal on displacing the block so force constant is 4K.
Hence, option (B) is correct.

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