Question

Lissajous figure obtained by combining

x = a sin wt and y = a sin $\left( \omega t + \frac{\pi}{4} \right)$will be :

• A. An ellipse
• B. A straight line
• C. A circle
• D. A parabola

Answer 1

Answer: (A)

An ellipse

Answer 2

$\frac{x}{a}$ = sinwt ; y = a sin$\left( \omega t + \frac{\pi}{4} \right)$

= a [sin wtcos $\frac{\pi}{4}$ + coswt sin$\frac{\pi}{4}$]

= $\frac{a}{\sqrt{2}}$ $\left\lbrack \frac{x}{a} + \sqrt{1–\frac{x^{2}}{a^{2}}} \right\rbrack$

Equation ® ellipse