A point performs simple harmonic oscillation of period T and the equation of motion is given by x = a sin ((ωt+π6)). After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity ?
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Explanation:
x = a sin ((ωt+π6) (Given)
Time period = T (Given)
dx/dt = aωcos (ωt + π/6)
Max velocity = aω
Therefore,
= aω/2 = aωcos (ωt + π/6)
= cos (ωt + π/6) = 1/2
= 60° or 2π/6 radian = 2π/T.t + π/6
= 2π/T.t = 2π/6 - π/6 = +π/6
Therefore, t = π/6 × T/2π
= T/12
Thus, after the elapse of 1/12 fraction of the time period the velocity of the point will be equal to half of its maximum velocity.
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