Question

The displacement y of a particle executing periodic motion is given by
$y=4{\cos }^2\left(t/2\right)\sin \left(100t\right)$
This expression may be considered to be a result of the super position of

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

The correct option is B 3

By using simple trigonometric formulas, we can easily see that it is the result of super position of 3 SHM's.
$y=4{\cos }^2\left(t/2\right)\sin \left(100t\right)\Rightarrow y=2(1+\cos t)\sin \left(100t\right)\Rightarrow y=2\sin \left(100t\right)+2\cos \left(t\right)\sin \left(100t\right)\Rightarrow y=2\sin \left(100t\right)+\sin \left(101t\right)-\sin \left(99t\right)$