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.