A point performs simple harmonic oscillation of period T and the equation of motion is given by x = a sin ω t + π 6 . After the elapse of what fraction of the time period the velocity of the point wil

Question

A point performs simple harmonic oscillation of period T and the equation of motion is given by x = a sin ω t + π 6 . After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity?

TestHub · Accepted Answer

x = a sin ω t + π 6 d ⁡ x d ⁡ t = a ω cos ω t + π 6 Maximum velocity = a ω ∴ a ω 2 = a ω cos ω t + π 6 ∴ cos ω t + π 6 = 1 2 ω t + π 6 = 6 0 ο = 2 π 6 rad ω t = 2 π 6 - π 6 = π 6 ∴ t = π 6 ω = π 6 × T ⁡ 2 π = T ⁡ 1 2 ∵ ω = 2 π T ⁡

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