One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to massless spring of spring constant K. A mass m hangs freely from the free end of the spring. The area of $$cross-section$$ and Young's modulus of the wire are A and Y respectively. If the mass is slightly pulled down and released, it will oscillate with a time period T equal to

Question

Infinity Learn · Accepted Answer

The wire may be treated as a string for which force constant  $$k1=ForceExtension=YAL$$   ∵$$Y=FA$$×LΔLSpring constant of the spring  $$k2=KHence$$ spring constant of the combination $$(series)keq=k1k2k1+k2=(YA/L)K(YA/L)+K=YAKYA+KL$$∵Time period  $$T=2$$$$π$$$$mk=2$$π$$(YA+KL)mYAK1/2$$

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