The displacement `y` of a particle periodic motion is given by
`y = 4 cos ((1)/(2) t) sin (1000 t)`
This expression may be considered as a result of the superposition of

Options

A. two
B. three
C. four
D. five

Answer

B

Explanation

`y =(4)/(2) [ 2 cos ^(2) ((t)/(2)) ] sin (1000 t)`
or ` y = 2 ( 1 + cos t) sin 1000 t`
or t = 2 sin 1000 t + 2 sin 1000 t cos t`
or ` y = 2 sin 1000 t + sin (1001 t) + sin (999 t)`
So , the given the expression is a result of the superposition of three independent harmonic motions .