The function x = A sin^2 omega t + B cos^2 om | vedclass

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(C) Using trigonometric identities,we rewrite the expression as:$x = \frac{A}{2}(1 - \cos 2\omega t) + \frac{B}{2}(1 + \cos 2\omega t) + \frac{C}{2} \

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If $A = B$ and $C = 0$

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(C) Using trigonometric identities,we rewrite the expression as:$x = \frac{A}{2}(1 - \cos 2\omega t) + \frac{B}{2}(1 + \cos 2\omega t) + \frac{C}{2} \sin 2\omega t$$x = \frac{A+B}{2} + \frac{B-A}{2} \cos 2\omega t + \frac{C}{2} \sin 2\omega t$For a function to represent $SHM$,it must be of the form $x = x_0 + A' \sin(2\omega t + \phi)$.$(A)$ If $A=0, B=0, C 
eq 0$,then $x = \frac{C}{2} \sin 2\omega t$. This represents $SHM$.$(B)$ If $A=-B, C=2B$,then $x = 0 + B \cos 2\omega t + B \sin 2\omega t$. This is a combination of sine and cosine waves of the same frequency,which represents $SHM$ with amplitude $|B\sqrt{2}|$.$(C)$ If $A=B, C=0$,then $x = \frac{A+A}{2} + \frac{A-A}{2} \cos 2\omega t + 0 = A$. Since $x$ is constant,it does not represent $SHM$.$(D)$ If $A=B, C=2B$,then $x = A + B \sin 2\omega t$. This represents $SHM$ oscillating about the mean position $x=A$.

The function $x = A \sin^2 \omega t + B \cos^2 \omega t + C \sin \omega t \cos \omega t$ does not represent $SHM$ for which of the following conditions?

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