Question

A mass-less spring of length 12 cm and stiffness 12 N/m is fixed at both ends. A small body of mass 27 gms is attached at a point 4 cm from one end. Find the period of small oscillations in the longitudinal direction.

• A. 0.12 sec
• B. 0.13 sec
• C. 0.14 sec
• D. 0.15 sec

Answer 1

The correct option is C 0.14 sec

When mass is attached at given position, it will become parallel connection of springs.


Equivalent stiffness,

$k^{\prime }=k_1+k_2=2k+\frac{3k}{2}=4.5k$

$\text{Now,}{\omega }_n=\frac{2\pi }{T}=\sqrt{\frac{k^{\prime }}{m}}$

$\therefore T=\frac{2\pi }{\sqrt{\frac{k^{\prime }}{m}}}=\frac{2\pi }{\sqrt{\frac{4.5\times 12}{27\times {10}^{-3}}}}=0.14\text{sec}$