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 A₀ from its natural length and then released. Find the time taken by the block to move from point ‘L’(at a distance $\frac{A}{2}$ from mean position) to point ‘M’.

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$\frac{2 π}{4} \sqrt{\frac{m}{k}}$

$\frac{2 π}{3} \sqrt{\frac{m}{k}}$

$\frac{2 π}{2} \sqrt{\frac{m}{k}}$

$\frac{2 π}{6} \sqrt{\frac{m}{k}}$

answer is A.

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Detailed Solution

$\frac{A_{0}}{2} \to 0 \Rightarrow \frac{T}{6}, 0 \to \frac{\sqrt{3} A_{0}}{2} \Rightarrow \frac{T}{6}, Total time t = \frac{T}{3}$

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