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JEE Main 201815 AprilEvening ShiftOnline
Exam
JEE Main
Year
2018
Date
15 April
Shift
Evening Shift
Mode
Online
Subject
Physics
Chapter
Oscillations

JEE Main 2018 · 15 April · Evening Shift · Online · Physics · Oscillations

Two simple harmonic motions, as shown, are at right angles. They...

Two simple harmonic motions, as shown, are at right angles. They are combined to form Lissajous figures. x(t)=Asin⁡(at+δ)x(t)=A \sin (a t+\delta) y(t)=Bsin⁡(bt)y(t)=B \sin (b t) Identify the correct match below

Options

  1. AParameters: A=B,a=2 b;δ=π2\mathrm{A}=\mathrm{B}, \mathrm{a}=2 \mathrm{~b} ; \delta=\frac{\pi}{2}; Curve: Circle
  2. BParameters: A=B,\mathrm{A}=\mathrm{B},\mathrm{a}=\mathrm{b};δ=π2;; \delta=\frac{\pi}{2} ; Curve: Line
  3. CParameters: A≠B,\mathrm{A} \neq \mathrm{B},\mathrm{a}=\mathrm{b};δ=π2;; \delta=\frac{\pi}{2} ; Curve: Ellipse
  4. DParameters: A≠B,\mathrm{A} \neq \mathrm{B},\mathrm{a}=\mathrm{b};δ=0; \delta=0; Curve: Parabola

Correct answer

C. Parameters: A≠B,\mathrm{A} \neq \mathrm{B},\mathrm{a}=\mathrm{b};δ=π2;; \delta=\frac{\pi}{2} ; Curve: Ellipse

Step-by-step solution

From the two mutually perpendicular S.H.M.'s, the general equation of Lissajous figure, \frac{x^2}{A^2}+\frac{y^2}{B^2}-\frac{2 x y}{A B} \cos \delta=\sin ^2 δ\deltax=Asin⁡(at+δ)y=Bsin⁡(bt+r)\begin{aligned}&x=A \sin (a t+\delta)\\ &y=B \sin (b t+r) \end{aligned}ClearlyClearlyA \neq B hence ellipse.
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