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  • Give answer! 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. Parameters Curve

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. Parameters Curve

  • Option 1)

    A ≠ B, a =b ; δ=0 Parabola

  • Option 2)

    A =B, a =b ; δ= π/2 Line

  • Option 3)

    A ≠ B, a =b ; δ= π/2 Ellipse

  • Option 4)

    A =B, a =2b ; δ= π/2 Circle

 

Answers (2)

best_answer

x=Asin(at+\delta )

y=ABsin(bt)

if a=b,

x=A\left [ sin(at).cos\delta +cos(at).sin\delta \right ]

sin(at)=\frac{y}{B}

\therefore \frac{x}{A}=\frac{y}{B}cos\delta +\sqrt{1-\frac{y^{2}}{B^{2}}}.sin\delta

\therefore \left ( \frac{x}{A}-\frac{y}{B}cos\delta \right )^{2}=\left ( {1-\frac{y^{2}}{B^{2}}} \right ).sin^{2}\delta

\frac{x^{2}}{A^{2}}+\frac{y^{2}}{B^{2}}-\frac{2xy}{AB}.cos\delta =sin^{2}\delta

IF \delta =\Pi /2,     \frac{x^{2}}{A^{2}}+\frac{y^{2}}{B^{2}}=1 \: \: \: (ellipse)


Option 1)

A ≠ B, a =b ; δ=0 Parabola

Option 2)

A =B, a =b ; δ= π/2 Line

Option 3)

A ≠ B, a =b ; δ= π/2 Ellipse

Option 4)

A =B, a =2b ; δ= π/2 Circle

Posted by

Avinash

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