A body performs angular simple harmonic motion about a fixed axis with angular amplitude θ₀ and time period T. At an instant its angular displacement is +θ₀/2 and it is moving towards the positive angular extreme +θ₀. How much additional time is required to reach the extreme?
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Question

A body performs angular simple harmonic motion about a fixed axis with angular amplitude θ₀ and time period T. At an instant its angular displacement is +θ₀/2 and it is moving towards the positive angular extreme +θ₀. How much additional time is required to reach the extreme?

Options

G1 Physics · Accepted Answer

Angular SHM has the same phase geometry as linear SHM. Write θ = θ₀ sinφ. At θ = θ₀/2 while moving towards the positive extreme, φ₁ = π/6. At θ = θ₀, φ₂ = π/2. Hence, Δφ = π/2−π/6 = π/3. Therefore, Δt = Δφ/ω = (π/3)/(2π/T) = T/6. Correct option: C.