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 A2from mean position) to point ‘M’.

A02→0⇒T6,0→3A02⇒T6, Total time t=T3

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 A2from mean position) to point ‘M’.

A02→0⇒T6,0→3A02⇒T6, Total time t=T3

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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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$\frac{2 π}{4} \sqrt{\frac{m}{k}}$

$\frac{2 π}{3} \sqrt{\frac{m}{k}}$

$\frac{2 π}{6} \sqrt{\frac{m}{k}}$

$\frac{2 π}{2} \sqrt{\frac{m}{k}}$

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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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