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Question

# A particle of mass m is attached to three springs A, B and C of equal force constants k as shown in figure. if the particle is pushed slightly against the spring C and released, find the time period of oscillation.

A
T=2πmk
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B
T=2π2mk
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C

T=2πm2k

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D
None of these
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Solution

## The correct option is C T=2π√m2k When the particle is displaced towards C by a small Deltax the extension in spring A and B is Δx√2 Net force on particle=kΔx+√(kΔx√2)2+(kΔx√2)2 =k.Δx+k.Δx=2kΔx For SHM we know, a=Fm=ω2Δx ⇒2kΔxm=ωΔx ⇒ω=√2km ⇒T=2π√m2k

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