Question

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. $\frac{\pi }{4}\sqrt{\frac{k}{m}}$

Answer 1

Answer: (C)

The total time from $A$ to $C$

$I_{AC}=t_{AB}+t_{BC}$
$=(T/4)+t_{BC}$
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 $t_{BC}=\frac{T}{12}$
$\Rightarrow t_{AC}=\frac{T}{4}+\frac{T}{12}=\frac{2\pi }{3}\sqrt{\frac{m}{k}}$