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. (a) Parameters A ≠ B, a = b; δ = 0; Curve Parabola (b) Parameters A = B, a = b; δ = π/2 Curve Line (c) Parameters A ≠ B, a = b; δ = π/2 Curve Ellipse (d) Parameters A = B, a = 2b; δ = π/2 Curve Circle

Answer: (c). (a) a = b, δ = 0: y/x = B/A, a straight line, not a parabola. (b) A = B, a = b, δ = π/2: x = Acos bt, y = Asin bt, a circle, not a line. (c) A ≠ B, a = b, δ = π/2: (x²)/(A²) + (y²)/(B²) = 1, an ellipse. Correct. (d) a = 2b: x = Acos 2bt = A(1 - 2y²/B²), a parabola, not a circle. So the answer is (c).

Two simple harmonic motions, as shown below, are at right angles… | JEE Main 2018 (15 Apr, Shift 2)

Q12JEE Main 2018 · 15 APR · SHIFT 2Medium

Damped, Forced Oscillations & Superposition

Two simple harmonic motions, as shown below, are at right angles. They are combined to form Lissajous figures.

x(t) = A sin (at + $\delta$ )

y(t) = B sin (bt)

Identify the correct match below.

Show answer and solution

Answer: (c)

(a) $a = b$ , $\delta = 0$ : $y/x = B/A$ , a straight line, not a parabola.
(b) $A = B$ , $a = b$ , $\delta = \frac{\pi}{2}$ : $x = A\cos bt$ , $y = A\sin bt$ , a circle, not a line.
(c) $A \neq B$ , $a = b$ , $\delta = \frac{\pi}{2}$ : $\frac{x^2}{A^2} + \frac{y^2}{B^2} = 1$ , an ellipse. Correct.
(d) $a = 2b$ : $x = A\cos 2bt = A(1 - 2y^2/B^2)$ , a parabola, not a circle.
So the answer is (c).

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Damped, Forced Oscillations & Superposition question from JEE Main 2018 (15 Apr, Shift 2)

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