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Y=A sin(ω t+φ₀) is the time-displacement equation of a SHM. At t=0 the displacement of the particle is Y=A/2 and it is moving along the negative x-direction. Then the initial phase angle φ₀ will be

Asked in JEE Main 25th Feb 2nd Shift 2021 · Displacement equation and phase

• (1) π/3
• (2) (2π)/3
• (3) (5π)/6
• (4) π/6

Step-by-step solution

Why the other options are wrong

• (1) Comes from cos φ₀=1/2. The equation is a sine, so it is sin φ₀ that must equal 1/2.
• (2) Has the correct negative velocity but gives sin φ₀=(√3)/2, that is a start at (A√3)/2.
• (4) Satisfies sin φ₀=1/2 but its cosine is positive, so the particle would be moving along +x.

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