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

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Answer & Solution

Correct Answer

(C) Parameters: \(A \ne B\), \(a\, = b\); \(\delta = \frac{\pi }{2}\); Curve : Ellipse

Detailed explanation

From the two mutually perpendicular \(S.H.M. 's\), the general equation of Lissajous figure

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

\(x = A\,\sin \,\left( {at + \delta } \right)\)

\(y = B\,\sin \,\left( {bt + r} \right)\)

Clearly \(A\ne B\) hence ellipse

Same subject

List \(I\)	List \(II\)
\(A\) Troposphere	\(I\) Approximate \(\quad 65-75\, km\) over Earth's surface
\(B\) E-Part of Stratosphere	\(II\) Approximate \(300\,km\) over Earth's surface
\(C\) \(F _2\)-Part of Thermosphere	\(III\) Approximate \(10\,km\) over Earth's surface
\(D\) \(F _2\)-Part of Thermosphere	\(IV\) Approximate \(100\,km\) over Earth's surface

From JEE Mains