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Question

A particle of mass m is attached to three identical springs A,B and C each of force constant k as shown in figure. If the particle of mass m in is pushed slightly against the spring A and released, then the time period of oscillation is


A
2π2mk
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B
2πm2k
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C
2πmk
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D
2πm3k
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Solution

The correct option is B 2πm2k
When the particle of mass m at O is pushed by y in the direction of A, the spring A will be compressed by y while springs B and C will be stretched by y=ycos45, so that the total restoring force on the mass m along OA,
Resultant force =FA+FBcos45+FCcos45
=ky+2kycos45
=ky+2k(ycos45)cos45=ky
where k=2k
T=2πmk=2πm2k
Hence, the correct answer is option (b).
Why this question?

Caution: Component followed by component- not to miss on.

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