Question

From a spring of spring constant ${}^{\prime }{k}^{\prime }$ , a small block of mass ${}^{\prime }{m}^{\prime }$ 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 ${}^{\prime }{L}^{\prime }$ to point ${}^{\prime }{M}^{\prime }$ .

• 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)

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