Oscillation on inline

A block of mass M = 1 kg is placed of a fixed rough incline of inclination \( \theta = \sin^{-1} \frac{7}{10} \) and coefficient of friction \( \mu = \frac{1}{ \sqrt{51}} \) connected to a spring of spring constant 100 N/m.

Initially the spring is in relaxed state with length = 10 cm. If the block is left to move, then, find the increment in the length (in cms) in spring when block is completely at rest.

Take \(g= 10 \text{ m/s}^2\).

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