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 $2 x_{0}$ 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_{A C} =t_{A B}+t_{B C} $
$=(T / 4)+t_{B C} $
where $T=$ time period of oscillation of spring mass system
$t_{B C}$ can be obtained from, $B C=A B \sin (2 \pi / T) t_{B C}$
Putting $\frac{B C}{A B}=\frac{1}{2}$ we obtain $t_{B C}=\frac{T}{12}$
$\Rightarrow t_{A C} = \frac{T}{4}+\frac{T}{12}=\frac{2 \pi}{3} \sqrt{\frac{m}{k}}$