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 :
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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 :

G1 Physics · Accepted Answer

Let the particle start from an extreme: x=A cosωt. In the first τ it travels a, so A[1−cos(ωτ)]=a. In the next τ it travels 2a in the same direction, so A[cos(ωτ)−cos(2ωτ)]=2a. Eliminating a gives cos(ωτ)=1/2, hence ωτ=π/3. Therefore T=2π/ω=6τ. Correct option: 4.