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Question:

Two simple harmonic motions, as shown, are at right angles. They are combined to form Lissajous figures. x(t) = Asin(at+δ) y(t) = Bsin(bt) Identify the correct match below. Parameters: A=B, a=2b; δ=π/2; Curve: Circle Parameters: A=B, a=b; δ=π/2; Curve: Line Parameters: A≠B, a=b; δ=0; Curve: Parabola Parameters: A≠B, a=b; δ=π/2; Curve: Ellipse

Parameters:A≠B,a=b;δ=π2; Curve: Ellipse

Parameters:A=B,a=b;δ=π2; Curve: Line

Parameters:A≠B,a=b;δ=0; Curve: Parabola

Parameters:A=B,a=2b;δ=π2; Curve: Circle

Solution:

Lissajous curves take common shapes depending on the variables in the expressions.
x = Asin(at+δ)
y = Bsin(bt+r)
If A≠B, a=b, we obtain ellipse