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Question

Two simple harmonic motions, as shown, are at right angles. They are combined to form Lissajous figures.
$$x(t)=A\sin { \left( at+\delta  \right)  } $$
$$y(t)=B\sin { \left( bt \right)  } $$
Identify the correct match below


A
Parameters: A=B,a=2b;δ=π2; Curve: Circle
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B
Parameters: A=B,a=b;δ=π2; Curve: Line
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C
Parameters: AB,a=b;δ=π2; Curve: Ellipse
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D
Parameters: AB,a=b;δ=0; Curve: Parabola
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Solution

The correct option is D Parameters: $$A\ne B,a=b;\delta =\cfrac { \pi }{ 2 } $$; Curve: Ellipse
Lissajous curves take common shapes depending on the variables in the expressions.
$$x=A\sin (at +\delta)$$
$$y = B \sin (bt + r)$$
If $$A \neq B$$ & $$a=b$$ we obtain ellipse

Physics

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