Question

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

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

Answer 1

Answer: (B)

three

$y=4{\cos }^2\left(\frac{t}{2}\right)\sin 1000t$
$=4\left(\frac{1+\cos t}{2}\right)\sin 1000t$
$=2\sin 1000t+2\cos t\sin 1000t$
$=2\sin 1000t+\frac{1}{2}(\sin 2t+\sin 2000t)$
$\therefore$ It's a superposition of three waves