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]sin 1000t` `[2cos^(2) theta =(1+COS^(2)theta)]` `y=2sin 1000 t+2sin 1000 t.cos t` `y=2sin 1000 t+sin 1001t+sin 999t` [as `2 sin A cos B=sin(A+B)+sin(A-B)` `:. `The given expression is the resultant of three INDEPENDENT simple HARMONIC MOTION.