A spring block system (mass = m, spring constant k) is placed on a smooth inclined plane (θ = angle of inclination). The plane isaccelerated horizontally with a such that the block does not loose contact with the plane. The time period of small oscillation of theblock is

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2πmk

2πmsin⁡θk

2πmgka

none of the above.

answer is A.

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Detailed Solution

x0∴ elongation in equilibrium ∴macos⁡θ+mgsin⁡θ=kx0For x = elongation from equilibrium net force =mgsin⁡θ+macos⁡θ−kx0+x =−k x (1)∴acc=−kxm ⇒T=2πmk

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