On a CRO (oscilloscope), a Lissajous figure appears as a straight line at 45° to the x-axis. If the X-plate is driven by x(t) = 2 sin(ωt), what Y-plate input y(t) produces this pattern?

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:Lissajous figures on a CRO result from applying sinusoidal voltages to the horizontal (X) and vertical (Y) plates. The observed shape encodes the relative amplitude, frequency, and phase between the two signals, which is a classic laboratory method to compare frequencies and phases. Given Data / Assumptions: X input: x(t) = 2 sin(ωt). Observed figure: straight line at 45° to the x-axis. Same frequency applied to both axes (standard Lissajous measurement for phase). Concept / Approach:A straight line indicates zero phase difference or 180° phase difference with amplitude ratios defining slope. A 45° line with positive slope requires equal amplitudes and zero relative phase (or both inverted together). Therefore, the Y-input must match the X-input in both amplitude and phase: y(t) = 2 sin(ωt). Any phase shift would rotate or thicken the line into an ellipse, and an amplitude difference would change the slope away from 45°. Step-by-Step Solution: Desired slope = +1 ⇒ |Y|/|X| = 1.Straight line (not ellipse) ⇒ phase difference Δφ = 0° (or 180° for negative slope).Hence y(t) = 2 sin(ωt) gives a +45° line. Verification / Alternative check: Plot x = 2 sin θ, y = 2 sin θ ⇒ y = x, a 45° line. Why Other Options Are Wrong: ±45° phase shifts produce an ellipse, not a perfect line; amplitude squaring (2^2) is dimensionally incorrect here. Common Pitfalls: Confusing slope sign with phase sign; forgetting equal amplitudes are required for 45°. Final Answer: 2 sin ωt

On a CRO (oscilloscope), a Lissajous figure appears as a straight line at 45° to the x-axis. If the X-plate is driven by x(t) = 2 sin(ωt), what Y-plate input y(t) produces this pattern?

More Questions from Measurements and Instrumentation

Discussion & Comments