Question

Which of the following is not simple harmonic function?

• A. $y=a\sin 2\omega t+b{\cos }^2\omega t$
• B. $y=a\sin \omega t+b\cos 2\omega t$
• C. $y=1-2{\sin }^2\omega t$
• D. $y=\left(\sqrt{a^2+b^2}\right)\sin \omega t\cos \omega t$

Answer 1

The correct option is B $y=a\sin \omega t+b\cos 2\omega t$

$y=asin2\omega t+bco{s}^2\omega t=asin2\omega t+b\frac{(cos2\omega t-1)}{2}=\frac{1}{2}(asin2\omega t+bcos2\omega t)-\frac{b}{2}$ which is SHM.

$y=1-2si{n}^2\omega t=cos2\omega t$ which is again SHM
$y=\left(\sqrt{a^2+b^2}\right)\sin \omega t\cos \omega t=asinx+bcosx$, which is again SHM
B can not be represented such way.