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JEE Main201815 Apr 2018Evening ShiftPhysicsOscillationsActual

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

Options

  1. AParameters: A = B , a =2 ~b ; = 2 ; Curve: Circle
  2. BParameters: A = B , a = b ; = 2 ; Curve: Line
  3. CParameters: A B , a = b ; = 2 ; Curve: Ellipse
  4. DParameters: A B , a = b ; =0 ; Curve: Parabola

Correct answer

C. Parameters: A B , a = b ; = 2 ; Curve: Ellipse

Step-by-step solution

From the two mutually perpendicular S.H.M.'s, the general equation of Lissajous figure, x^2 A^2 + y^2 B^2 - 2 x y A B = ^2 aligned &x=A (a t+ ) &y=B (b t+r) aligned Clearly A B hence ellipse.

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