Question

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 ?

Answer 1

this is your answer...and ...

Answer 2

Answer:

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.