Question

From a spring of spring constant $'k'$ , a small block of mass $'m'$ is attached and the system is placed on a smooth horizontal surface as shown in the figure. The spring is compressed by distance $A_{0}$ from its natural length and then released. Find the time taken by the block to move from point $'L'$ to point $'M'$ .

• A. $\frac{\pi }{4}\sqrt{\frac{m}{k}}$
• B. $\frac{\pi }{3}\sqrt{\frac{m}{k}}$
• C. $\frac{\pi }{2}\sqrt{\frac{m}{k}}$
• D. $\frac{\pi }{6}\sqrt{\frac{m}{k}}$

Answer 1

Answer: (C)

$\phi=\frac{\pi }{2}$
$\frac{t}{T}=\frac{\pi / 2}{2 \pi }$
$\therefore t=T/4=\frac{\pi }{2}\sqrt{\frac{m}{k}}$