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(A) When a mass $m$ is suspended from a wire,the wire acts like a spring with a spring constant $k$. From Hooke's Law,the tension $T$ in the wire for

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$\frac{1}{2 \pi}\left(\frac{YA}{mL}\right)^{\frac{1}{2}}$

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(A) When a mass $m$ is suspended from a wire,the wire acts like a spring with a spring constant $k$. From Hooke's Law,the tension $T$ in the wire for an extension $x$ is given by $T = \frac{YA}{L} x$. Comparing this with the spring force equation $F = kx$,we find the effective spring constant $k = \frac{YA}{L}$. The frequency of oscillation $f$ for a mass-spring system is given by $f = \frac{1}{2 \pi} \sqrt{\frac{k}{m}}$. Substituting the value of $k$,we get $f = \frac{1}{2 \pi} \sqrt{\frac{YA}{mL}}$.

$A$ small mass $m$ is suspended at the end of a wire having negligible mass,length $L$,and cross-sectional area $A$. The frequency of oscillation for the $S.H.M.$ along the vertical line is ($Y =$ Young's modulus of the wire).

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