A block of mass m placed on a smooth horizontal floor is connected with two light springs of spring constant k. The angular frequency of small horizontal oscillation of the block along horizontal plane is N rad/s. Find N. (Given: m=41 kg, k=100N/m, $θ = 37^{0}$ )

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answer is 2.

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Detailed Solution

When displaeed by dx towards right, then elongation of left spring = $d x \cos θ$

Restoring force= $- (k d x + k d x \cos^{2} θ)$

$m a = - k (1 + \cos^{2} θ) d x$

$a = - \frac{k (1 + \cos^{2} θ)}{m} d x$

$∴ ω = \sqrt{\frac{k (1 + \cos^{2} θ)}{m}}$

$ω = \sqrt{\frac{100 (1 + \cos^{2} 37^{0})}{41}} = 2 r a d / s$

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