The displacement of a particle executing periodic motion is given by y= 4cos^(2)((t)/(2))sin(1000t). Find independent constituent simple harmonic motions.

The displacement of a particle executing periodic motion is given by y

1.	The displacement of a particle executing periodic motion is given by y= 4cos^(2)((t)/(2))sin(1000t). Find independent constituent simple harmonic motions.
Answer» Solution :`y= 4COS^(2)((t)/(2))sin(1000t)` `y= 2[1+ cost]sin1000t` `[2COS^(2)THETA= (1+cos2theta)]` `y= 2sin1000t +2sin1000t.cost` `y= 2sin1000t+sin1001 t+sin999t` [as 2 sin A COS B = sin (A+B) + sin (A-B)] `:.` The given expression is the resultant of THREE independent simple harmonic motion.