MCQ
Two mutually perpendicular simple harmonic vibrations have same amplitude, frequency and phase. When they superimpose, the resultant form of vibration will be
- AA circle
- BAn ellipse
- ✓A straight line
- DA parabola
✓
Answer
Correct option: C.
A straight line
If $y_1=a_1 \sin \omega t$ and $y_2=a_2 \sin (\omega t+0)=a_2 \sin \omega t$
$\Rightarrow \frac{y_1^2}{a_1^2}+\frac{y_2^2}{a_2^2}-\frac{2 y_1 y_2}{a_1 a_2}=0$
$\Rightarrow y_2=\frac{a_2}{a_1} y_1$
This is the equation of straight line.
$\Rightarrow \frac{y_1^2}{a_1^2}+\frac{y_2^2}{a_2^2}-\frac{2 y_1 y_2}{a_1 a_2}=0$
$\Rightarrow y_2=\frac{a_2}{a_1} y_1$
This is the equation of straight line.
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