A point performs simple harmonic oscillation of period

A point performs simple harmonic oscillation of period T and the equation of motion is given by x = a sin (ωt + 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?

We have , x = a sin		ωt +	π
			6

∴ Velocity , v =	dx	= aω cos		ωt +	π
	dt				6

Maximum velocity = aω
According to question,

	aω	= aω cos		ωt +	π
	2				6

or cos		ωt +	π		=	1	= cos 60° or cos	π
			6			2		3

⇒ ωt +	π	=	π
	6		3

⇒ ωt =	π	-	π	or ωt =	π
	3		6		6

or	2π	.t =	π	⇒ t =	T
	T		6		12