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Question

# A particle of mass m is attached to three identical massless springs of spring constant k as shown in the figure. The time period of vertical oscillation of the particle is:

A
2πmk
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B
2πm2k
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C
2πm3k
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D
πmk
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Solution

## The correct option is B 2π√m2kWhen 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 spring B and C will be stretched by y′=ycos45∘. So, that the total restoring force on the mass m is along OAFnet=FA+FBcos45∘+FCcos45∘=ky+2ky′cos45∘=ky+2k(ycos45∘)cos45∘=2kyAlso, Fnet=k′y⇒k′y=2ky⇒k′=2kT=2π√mk′=2π√m2k

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