Q.
An object suspended from a spring exhibits oscillations of period T. Now the spring is cut in two halves and the same object is suspended with two halves as shown in figure. The new time period of oscillation will become
A) $\frac{T}{2\sqrt{2}}$
B) $\frac{T}{2}$
C) $\frac{T}{\sqrt{2}}$
D) 2T
Explanation
(b) Let $k$ be the spring constant of each half part of the spring. For a complete spring, the spring constant $k^{'} = k/2$
(springs in series). When two splitted parts of a spring are connected to the body, then the springs are in parallel. Their effective spring constant, $k^{'} = k + k = 2k$
As $T = 2\pi\sqrt{\frac{m}{k}}\ \ \ or\ \ \ T \propto \frac{1}{\sqrt{k}}$
$\therefore\ \ \frac{T^{'}}{T} = \sqrt{\frac{k/2}{2k}} = \frac{1}{2}\ or\ T^{'} = \frac{T}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.