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

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$2 π \sqrt{\frac{m}{k}}$

none of the above.

$2 π \sqrt{\frac{msin θ}{k}}$

$2 π \sqrt{\frac{mg}{ka}}$

answer is A.

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Detailed Solution

$x_{0} ∴$ elongation in equilibrium
$∴ macos θ + mgsin θ = {kx}_{0}$
For x = elongation from equilibrium
$net force = mgsin θ + macos θ - k (x_{0} + x)$
$= - k x (1)$
$∴ acc = - \frac{kx}{m} \Rightarrow T = 2 π \sqrt{\frac{m}{k}}$

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