Q.
As shown in figure, a simple harmonic motion oscillator having identical four springs has time period
A) $T = 2\pi\sqrt{\frac{m}{4k}}$
B) $T = 2\pi\sqrt{\frac{m}{2k}}$
C) $T = 2\pi\sqrt{\frac{m}{k}}$
D) $T = 2\pi\sqrt{\frac{2m}{k}}$
Explanation
(c) [image:14_image57.emf]
Spring $P$ and $Q,R$ and $S$ are in parallel
then, $x = k + k = 2k\ \ \ $ [for$\ P,Q\rbrack$
and $y = k + k = 2k\ \ \ \ \ \ \ $ [for$\ R,S\rbrack$
$x$ and $y$ both in series
$\therefore\frac{1}{k^{''}} = \frac{1}{x} + \frac{1}{y} = \frac{1}{k}$
Time period$\ T = 2\pi\sqrt{\frac{m}{k^{''}}} = 2\pi\sqrt{\frac{m}{k}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.