Question

In the equations below, A, B, $\omega$ and $\varphi$ are constants; $y$ and $t$ are variables; $t$ represents time. Only one of the following equations does not represent SHM. Which one is that?

• A. $y=Asin\omega t$
• B. $y=Bcos\omega t$
• C. $y=Asin\omega t+Bcos\omega t$
• D. $y=Asin\omega t+Bcos\left(2\omega t\right)$

Answer 1

The correct option is D $y=Asin\omega t+Bcos\left(2\omega t\right)$

A linear combination of coherent simple harmonic motions would result in another simple harmonic motion.

But the combination of two incoherent simple harmonic motions($Asin\omega t,Bcos\left(2\omega t\right)$) is NOT an SHM.

Hence the answer is option D.