Question

A wire is clamped horizontally between two rigid support and a small mass is hanged from middle of the wire. The mass is displaced a little in vertical direction -

• A. Mass will undergo S.H.M for all value of ‘x’ (large or small)
• B. Mass will not undergo S.H.M for any value of ‘x’ (large or small)
• C. Mass will undergo S.H.M. only if value of ‘x’ is very small
• D. Mass will undergo periodic motion

Answer 1

Answer: (B), (D)

The correct options are
B Mass will not undergo S.H.M for any value of ‘x’ (large or small)
D Mass will undergo periodic motion

Let ‘x’ be the displacement from mean position ‘P’ shown in figure.

Restoring force $=\text{2T sin}\theta$
$={\text{2.K. x sin}}^2\theta$
$=2.K.\frac{x^3}{a^2}$
Thus restoring force is proportional to $x^3$.
Hence mass will not undergo S.H.M. but it will undergo periodic motion.