A particle starts from the mean position and moves towards the positive extreme. Let t₁ be the time required to move from x = 0 to x = A/2, and let t₂ be the time required to move from x = A/2 to x = A. If t₂/t₁ = N, find N.
Physics · Simple Harmonic Motion · displacement ,velocity and acceleration ,phasor diagram
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Question

A particle starts from the mean position and moves towards the positive extreme. Let t₁ be the time required to move from x = 0 to x = A/2, and let t₂ be the time required to move from x = A/2 to x = A. If t₂/t₁ = N, find N.

Physics · Simple Harmonic Motion · displacement ,velocity and acceleration ,phasor diagram

G1 Physics · Accepted Answer

From mean position to A/2, phase changes from 0 to π/6. Therefore, t₁ = T/12. From A/2 to A, phase changes from π/6 to π/2, so t₂ = T/6. Hence, t₂/t₁ = (T/6)/(T/12) = 2. Therefore, N = 2.