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

Options

A. Parameters: A = B, a = 2b, `delta=(pi)/(2)`, Curve : Circle
B. Parameters: A = B, a = b, `delta=(pi)/(2)`, Curve: Line
C. Parameters: `A ne B,a=b, delta=(pi)/(2)`, Curve: Ellipse
D. Parameters: `A ne B,a=b, delta=0`, Curve: Parabola

Answer

C

Explanation

From the two mutually perpendicular S.H.M..s, the general equation of Lissajous figure,
`(x^(2))/(A^(2))+(y^(2))/(B^(2))-(2xy)/(AB)cos delta=sin^(2)delta`
`x=A sin(at+delta)" "y=B sin(bt+r)`
Clearly `A ne B` hence ellipse.