Question 369: Oscillations

Question

One end of a spring of force constant $$k$$ is fixed to a vertical wall and other to a body of mass $$m$$ resting on a smooth horizontal surface. There is another wall at a distance $$x_0$$ from the body. The spring is then compressed by $$2 x_0$$ and released. The time taken to stike the wall is

Accepted Answer

The total time from $$A$$ to $$C$$
$$t_{A C}=t_{A B}+t_{B C}=\frac{T}{4}+t_{B C}$$
where, $$T=$$ Time period of oscillation of spring-mass system. $$t_{B C}$$ can be given by
$$B C=A B \sin \left(\frac{2 \pi}{t}ight) t_{B C}$$
Putting $$\frac{B C}{A B}=\frac{1}{2}$$, we get
$$\begin{aligned}
t_B & =\frac{T}{12} \
t_{A C} & =\frac{2 \pi}{3} \sqrt{\frac{m}{k}}
\end{aligned}$$

Answer

$$\frac{\pi}{6} \sqrt{\frac{m}{k}}$$

Answer

$$\sqrt{\frac{m}{k}}$$

Answer

$$\frac{2 \pi}{3} \sqrt{\frac{m}{k}}$$

Answer

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

Oscillations

One end of a spring of force constant $k is fixed to a vertical wall and other to a body of mass m resting on a smooth horizontal surface. There is another wall at a distance x_0 from the body. The spring is then compressed by 2 x_0$ and released. The time taken to stike the wall is

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