Function $x$ = $A sin^2 wt + B cos^2 wt + C sin wt \ cos wt$ does not represents $SHM$ for this condition
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$\mathrm{x}=\frac{\mathrm{A}}{2}(1-\cos 2 \omega \mathrm{t})+\frac{\mathrm{B}}{2}(1+\cos 2 \omega \mathrm{t})+\frac{\mathrm{C}}{2} \sin 2 \omega \mathrm{t}$
$(1)$ For $\mathrm{A}=0, \mathrm{B}=0 ;\left(\mathrm{x}=\frac{\mathrm{C}}{2} \sin 2 \omega \mathrm{t}\right)$
$(2)$ For $A=-B$ and $C=2 B$
$\mathrm{x}=\mathrm{B} \cos 2 \omega \mathrm{t}+\mathrm{B} \sin 2 \omega \mathrm{t} ;$ Amplitude $=|\mathrm{B} \sqrt{2}|$
$(3)$ For $\mathrm{A}=\mathrm{B} ; \mathrm{C}=0 ; \mathrm{x}=\mathrm{A}$
Hence this will not represent $SHM$
$(d)$ For $A=B, C=2 B ; x=B+B \sin 2 \omega t$
it also represents $SHM.$
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