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13. oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics13. oscillations1 Mark
MCQ
Function $x$ = $A sin^2 wt + B cos^2 wt + C sin wt \  cos wt$ does not represents $SHM$ for this condition
  • A
    If $A =0$; $B =0$ and $C \ne 0$
  • B
    If $A = -B ; C = 2B,$ amplitude =$\left| {B\sqrt 2 } \right|$
  • ✓
    If $A = B$ ; $C =0$
  • D
    If $A =B$ ; $C = 2B,$ amplitude =$\left| B \right|$
✓

Answer

Correct option: C.
If $A = B$ ; $C =0$
c
$\mathrm{x}=\frac{\mathrm{A}}{2}(1-\cos 2 \omega \mathrm{t})+\frac{\mathrm{B}}{2}(1+\cos 2 \omega \mathrm{t})+\frac{\mathrm{C}}{2} \sin 2 \omega \mathrm{t}$

$(1)$ 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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