Q. A mass $m = 100\ g$ is attached at the end of a light spring which oscillates on a frictionless horizontal table with an amplitude equal to $0.16\ metre$ and time period equal to 2 $sec.$ Initially the mass is released from rest at $t = 0$ and displacement $x = - 0.16\ metre.$ The expression for the displacement of the mass at any time $t$ is
A) $x = 0.16\cos{(\pi t)}$
B) $x = - 0.16\cos{(\pi t)}$
C) $x = 0.16\sin{(\pi t + \pi)}$
D) $x = - 0.16\sin{(\pi t + \pi)}$
Explanation
(b) Standard equation for given condition
$x = a\cos\frac{2\pi}{T}t \Rightarrow x = - 0.16\cos{(\pi t)}$
[As $a = - 0.16\ meter,\ T = 2\ s$]
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.