Question

Two sinusoidal signals $p({\omega }_1,t)=Asin{\omega }_{1}tandq({\omega }_2,t)$ are applied to X and Y inputs of a dual channel CRO. The Lissajous figure displayed on the screen is shown below:
The signal $q({\omega }_2,t)$ will be represented as

• A. $q({\omega }_2,t)=Asin{\omega }_{2}t,{\omega }_2=2{\omega }_1$
• B. $q({\omega }_2,t)=Asin{\omega }_{2}t,{\omega }_2=2{\omega }_1/2$
• C. $q({\omega }_2,t)=Acos{\omega }_{2}t,{\omega }_2=2{\omega }_1$
• D. $q({\omega }_2,t)=Acos{\omega }_{2}t,{\omega }_2={\omega }_{1/2}$

Answer 1

The correct option is D $q({\omega }_2,t)=Acos{\omega }_{2}t,{\omega }_2={\omega }_{1/2}$

Here,
$p\left({\omega }_{1}t\right)=ASin{\omega }_{1}t$

$y_1-line$ cut '4' times the Lissajous pattern
$x_1-line$ cut '2' times the Lissajous pattern


Maximum number of intersection of a horizontal line with Lissajous pattern

$\frac{{\omega }_y}{{\omega }_x}=\frac{maximumnumberofintersectionbyhorizontalline}{maximumnumberofintersectionbyverticalline}$

$\therefore \frac{{\omega }_y}{{\omega }_x}=\frac{2}{4}=\frac{1}{2}$

$\therefore {\omega }_x=2{\omega }_y$

${\omega }_1=2{\omega }_2$

$andq({\omega }_2,t)willleadp({\omega }_1,t)by{90}^{\circ }astraceisacircle,$

$q({\omega }_2,t)=Asin({\omega }_{2}t+{90}^{\circ })$
$q({\omega }_2,t)=Acos{\omega }_{2}t$