# The displacement y of a particle executing periodic motion id given by…

Q: The displacement y of a particle executing periodic motion id given by
y = 4 cos2(t/2)sin (1000t)
This expression may considered to be a result of the superposition of ………………… independent harmonic motion.

(a) two

(b) three

(c) four

(d) five

Ans: (b)

Sol: $\large y = 4 cos^2 (\frac{t}{2}) sin(1000 t)$

$\large y = 2 (2 cos^2 (\frac{t}{2})) sin(1000 t)$

$\large y = 2 (1 + cost) sin (1000 t)$

$\large y = 2 sin(1000 t) + 2 cost sin(1000 t)$

$\large = 2 sin(1000 t) + sin(1001 t) + sin(999 t)$

This is the result of the superposition of three independent harmonic motion.