A point mass m is suspended at the end of a mass less wire of length l and cross section A. If Y is the Young’s modulus for the wire, obtain the frequency of oscillation for the simple harmonic motion along the vertical line.

Dear Student,
Please find below the solution to your problem.

Frequency depends on spring factor and inertia factor.
In this case, stress =mg/A​
Strain =l/L​ (where l is extension)
Now, Young's modulus Y is given by
Y=stress/strain​ = (mg/A)/(l/L)​
mg = YAl/L
So, kl = YAl/L ​(∵mg=kl) (k is force constant)
∴k = YA/L​
Now, frequency is given by
n= (1/2π)*(​√k/m)​
=(1/2π)*(​√YA/Lm)
​
Thanks and Regards