A particle executes SHM of period 8 s. At t = 0 it is at the mean position. Find the ratio of distance covered in the first second to that covered in the second second.
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Question

A particle executes SHM of period 8 s. At t = 0 it is at the mean position. Find the ratio of distance covered in the first second to that covered in the second second.

G1 Physics · Accepted Answer

With T=8 s and starting from the mean, x=A sin(πt/4). Distance in the first second is d₁=A sin(π/4)=A/√2. At t=2 s the particle reaches A, so distance in the second second is d₂=A−A/√2. Thus d₁/d₂=(1/√2)/(1−1/√2)=√2+1. Correct option: 4.