Question

# Which of the following is not simple harmonic function?

A
y=asin2ωt+bcos2ωt
B
y=asinωt+bcos2ωt
C
y=12sin2ωt
D
y=(a2+b2)sinωtcosωt

Solution

## The correct option is B $$y=a\sin \omega t+b\cos 2\omega t$$$$y=asin2\omega t + bcos^2 \omega t = asin2\omega t +b \dfrac {(cos2\omega t -1)}{2}= \dfrac{1}{2} (asin2\omega t + bcos2 \omega t) - \dfrac {b}{2}$$   which is SHM.$$y=1-2sin^2\omega t = cos2\omega t$$ which is again SHM$$y=\left ( \sqrt{a^{2}+b^{2}} \right )\sin \omega t\cos \omega t=asinx+bcosx$$, which is again SHMB can not be represented such way. Physics

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