Question

Two mutually perpendicular simple harmonic vibrations have the same amplitude, frequency and phase. When they superimpose, the resultant form of vibration will be

• A. a circle
• B. an ellipse
• C. a straight line
• D. a parabola

Answer 1

The correct option is C a straight line

If ,$y_1=a_1\sin \omega t{y}_2=a_2\sin (\omega t+0)=a_2\sin \omega t\Rightarrow \frac{y_1^2}{a_1^2}+\frac{y_2^2}{a_2^2}-\frac{2y_1{y}_2}{a_1{a}_2}=0\Rightarrow y_2=\frac{a_2}{a_1}{y}_1$
which is the equation of straight line of the form $y=mx$.