Question

Two simple harmonic motions, as shown below, are at right angles. They are combined to form Lissajous figures.
$x(t)=A\sin (at+\delta )$
$y(t)=B\sin (bt)$
Identify the correct match below.

• A. Parameters $-A\ne B,a=b;\delta =0$
  Curve - Parabola
• B. Parameters - $A=B,a=b;\delta =\pi /2$
  Curve - Line
• C. Parameters - $A\ne B,a=b;\delta =\pi /2$
  Curve - Ellipse
• D. Parameters $-A=B,a=2b;\delta =\pi /2$
  Curve - Circle

Answer 1

Answer: (C)

The given simple harmonic motions to form Lissajous figures are $x(t)=A\sin (at+\delta )$ and $y(t)=B\sin (bt)$.
For parabola, conditions should be$A=B$ or $A\ne B,a=2b,\delta =\pi /2$
For line, conditions should be$A=B,a=b,\delta =\pi$
For cir ould be$A=B,a=b;\delta =\pi /2$
For ellipse, condition should be$A\ne B,a=b;\delta =\pi /2$
Therefore, we obtain an ellipse.