A particle starts simple harmonic motion from the mean position.

A particle starts simple harmonic motion from the mean position. Its amplitude is A and time period is T.What is its displacement when its speed is half of its maximum speed

v_max = Aω when v =	v_max	=	Aω
	2		2

v = ω √A² - y²

⇒	Aω	= ω √A² - y² ⇒ y = ±	√3	A
	2		2

[ Alt : The displacement at which the speed is n times the maximum speed is given by y = a √1 - n² ]

	√2	A
	3

	A
	√2