One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to mass less 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

Let us beat the wire as a $$strin8$$. The force constant is given $$byk1=$$ force  extension $$=YAL$$ ∵$$Y=FA$$×LΔL or FΔ$$L=YAL$$ The wire of force constant $$k1$$ and spring of force constant k are in series. The combined force constant $$k2$$, is given by $$k2=k1kk1+k=(YA/L)(k)(YA/L)+k=YAkYA+kL$$ now $$T=2$$$$π$$$$mk2=2$$π$$(YA+kL)mYAk1/2$$

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