Question

The displacement y of a particle executing periodic motion is given by
$y=4{cos}^2\left(\frac{1}{2}t\right)sin\left(1000t\right)$
This expression may be considered to be a result of the superposition of

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

Answer 1

Answer: (B)

three

$y=4{\cos }^2\left(\frac{t}{2}\right)\sin 1000t$

$\Rightarrow y=2(1+\cos t)\sin 1000t$

$\Rightarrow y=2\sin 1000t+2\cos t\sin 1000t$

$\Rightarrow y=2\sin 1000t+\sin 999t+\sin 1001t$

It is a sum of three SHM