A particle moves with simple harmonic motion in a straight line. In first τ s , after starting from rest it travels a distance a, and in next τ s it travels 2a, in same direction, then :

Question

A particle moves with simple harmonic motion in a straight line. In first τ s , after starting from rest it travels a distance a, and in next τ s it travels 2a, in same direction, then :, Amplitude of motion is 3a, Time period of oscillations is 8 τ, Amplitude of motion is 4a, Time period of oscillations is 6 τ

MARKS App · Accepted Answer

x = - A cos ω t - A + a = - A cos ω τ ...(i) - A + 3 a = - A cos ω 2 τ ...(ii) ∴ - 1 + a A = - cos ω τ ...(iii) and - 1 + 3 a A = - cos 2 ω τ ...(iv) Adding (iii) and (iv) 2 = 3 cos ω τ - 2 cos 2 ω τ + 1 ∴ 2 cos 2 ω τ - 3 cos ω τ + 1 = 0 ∴ cos ω τ = 1 2 ∴ ω τ = π 3 ∴ T = 6 τ

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