A particle of mass m is attached to three identical springs A, B, C each of force constant k as shown. If the particle is pushed slightly against the spring A and released, find the time period of oscillations
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 Sol Let the particle of mass m at O be pushed downward against spring A. Then the forces produced in springs B and C will be in the directions shown. If y is the instantaneous compression of spring A, then B and C will be stretched by ycos45∘ each. ∴ Total restoring force on mass m along AO will be F=FA+FBcos45∘+FCcos45∘ =ky+(kycos45∘)cos45∘+(kycos45∘)cos45∘ =ky(1+2cos245∘) =ky(1+212)=2ky ⇒ a=2kym∴T=2π√m2k ∴T=2π√m2k