A body is executing S.H.M. When the displacements from the

A body is executing S.H.M. When the displacements from the mean position are 4cm and 5 cm, the corresponding velocities of the body are 10 cm per sec and 8 cm per sec. Then the time period of the body is

For S.H.M., Velocity,
v = ω √a² - x² at displacement x.
⇒ 10 = ω √a² - 16 ..........(1)
and 8 = ω √a² - 25 ..........(2)

Dividing ,	5²	=	a² - 16	=	25
	4²		a² - 25		16

or , 16a² - 256 = 25a² - 625 ⇒ 9a² = 369

∴ a² =	369
	9

Putting this value in equation (2) mentioned above,

or , ω =	10 × 3	= 2 radian / sec
	15

Time period =	2π	=	2π	= π sec
	ω		2