Y = A sin(ωt + φ₀) is the displacement–time equation of an SHM. At t = 0, Y = A/2 and the particle moves in the negative x-direction. The initial phase φ₀ is:
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Question

Y = A sin(ωt + φ₀) is the displacement–time equation of an SHM. At t = 0, Y = A/2 and the particle moves in the negative x-direction. The initial phase φ₀ is:

G1 Physics · Accepted Answer

At t=0, A sinφ₀=A/2, so sinφ₀=1/2. The particle moves in the negative x-direction, so v=Aω cosφ₀<0, which requires cosφ₀<0. Therefore φ₀ lies in quadrant II: φ₀=5π/6. Correct option: 3.