Question

Two simple harmonic motions, as shown below, are at right angles. They are combined to form lissajous figures. X(t)=a sin (at+) y(t)=b sin (bt) identify the correct match below

Answer 1

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

Option 1) A ≠ B, a =b ; δ=0 Parabola

Option 2) A =B, a =b ; δ= π/2 Line

Option 3) A ≠ B, a =b ; δ= π/2 Ellipse

Option 4) A =B, a =2b ; δ= π/2 Circle

from the two mutually perpendicular simple harmonic motions , The general equation of Lissajous figure,
$\frac{x^2}{A^2}+\frac{y^2}{B^2}-\frac{2xy}{AB}cos\delta=sin^2\theta$

here, $x=Asin(at+\delta)$
$y=Bsin(bt+\gamma)$

it is clear that, A ≠ B it is equation of ellipse .

hence, option (3) is correct.