A simple harmonic oscillator has an amplitude A and time

A simple harmonic oscillator has an amplitude A and time period T. The time required by it to travel from x = A to x = A/2 is

For S.H.M., x = A sin			2π	. t
			T

When x = A , A = A sin			2π	. t
			T

∴ sin			2π	. t		= 1
			T

⇒ sin

2π

. t

= sin

⇒ t = (T / 4)

When x =	A	,	A	= A sin			2π	.t
	2		2				T

or , sin	π	= sin			2π	.t		or t = (T / 12)
	6				T

Now, time taken to travel from x = A tox = A/2 is (T/4 – T/12) = T/6