Horizontal input to a scope is E_m sin (ωt) V, vertical input to that scope is E_m sin (ωt + 30°) V. What is the Lissajous pattern in that CRO?

Concept:

When two sinusoidal signals of the same frequency and magnitude are applied two both pairs of deflecting plates of CRO, the Lissajous pattern changes with the change of phase difference between signals applied to the CRO

When 0 < ϕ < 90o or 270o < ϕ < 360o 

The Lissajous pattern is of the shape of an Ellipse having a major axis passing through the origin from the first quadrant to the third quadrant.

 When 90o < ø < 180o or 180o < ø < 270o

The Lissajous Pattern is of the shape of an Ellipse having a major axis passing through the origin from the second quadrant to the fourth quadrant.

Explanation:

The given inputs are: Em sin (ωt) V, Em sin (ωt + 30°) V

The phase difference between both the inputs = 30°

The Lissajous pattern on the screen of a CRO is an ellipse with a major axis in quadrant 1 and quadrant 3. 

Important Points