(C) The general equation for the superposition of two perpendicular simple harmonic motions is given by:$\frac{x^2}{A^2} + \frac{y^2}{B^2} - \frac{2xy

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Parameters: $A \neq B$,$a = b$,$\delta = \frac{\pi}{2}$; Curve: Ellipse

(C) The general equation for the superposition of two perpendicular simple harmonic motions is given by:$\frac{x^2}{A^2} + \frac{y^2}{B^2} - \frac{2xy}{AB} \cos \delta = \sin^2 \delta$For option $C$: Given $a = b$ and $\delta = \frac{\pi}{2}$,the equation becomes:$\frac{x^2}{A^2} + \frac{y^2}{B^2} - \frac{2xy}{AB} \cos(\frac{\pi}{2}) = \sin^2(\frac{\pi}{2})$$\frac{x^2}{A^2} + \frac{y^2}{B^2} = 1$Since $A \neq B$,this is the standard equation of an ellipse.Therefore,option $C$ is the correct match.

Class 11 Physics Oscillations Superposition of S.H.M.

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

JEE MAIN 2018 All JEE MAIN

A
Parameters: $A = B$,$a = 2b$,$\delta = \frac{\pi}{2}$; Curve: Circle
B
Parameters: $A = B$,$a = b$,$\delta = \frac{\pi}{2}$; Curve: Line
C
Parameters: $A \neq B$,$a = b$,$\delta = \frac{\pi}{2}$; Curve: Ellipse
D
Parameters: $A \neq B$,$a = b$,$\delta = 0$; Curve: Parabola

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

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