A particle starts simple harmonic motion from the mean position. Its amplitude is a and time period is T. What is its displacement when its speed is half of its maximum speed?
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A particle starts simple harmonic motion from the mean position. Its amplitude is a and time period is T. What is its displacement when its speed is half of its maximum speed?

G1 Physics · Accepted Answer

Step 1: For SHM, v = ω√(a² − x²) and vₘₐₓ = ωa. Step 2: Given |v| = vₘₐₓ/2, hence √(a² − x²) = a/2. Step 3: Square: a² − x² = a²/4, so x² = 3a²/4. Step 4: The particle starts at the mean and first moves to the positive side, so x = √3a/2. Final answer: (B) √3a/2.