Q.
One end of a spring of force constant k is fixed to a vertical wall and the other to a block of mass m resting on a smooth horizontal surface. There is another wall at a distance $x_{0}$ from the black. The spring is then compressed by $2x_{0}$ and released. The time taken to strike the wall is
A) $\frac{1}{6}\pi\sqrt{\frac{k}{m}}$
B) $\sqrt{\frac{k}{m}}$
C) $\frac{2\pi}{3}\sqrt{\frac{m}{k}}$
D) $\frac{\pi}{4}\sqrt{\frac{k}{m}}$
Explanation
(c) The total time from $A$ to $C$
$t_{AC} = t_{AB} + t_{BC}$
$= \left( \frac{T}{4} \right) + t_{BC}$
Where $T =$time period of oscillation of spring mass system
$t_{BC}$ can be obtained from, $BC = AB\sin{(2\pi/T)}t_{BC}$
Putting $\frac{BC}{AB} = \frac{1}{2}$ we obtain $t_{BC} = \frac{T}{12}$
$\Rightarrow \ \ \ t_{AC} = \frac{T}{4} + \frac{T}{12} = \frac{2\pi}{3}\sqrt{\frac{m}{k}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.