A particle is subjected to two mutually perpendicular simple harmonic motions such that its `X` and `y` coordinates are given by `X=2 sin omegat` , `y=2 sin (omega+(pi)/(4))`
The path of the particle will be:

Options

A. an ellipse
B. a straight lin
C. a parabloa
D. a circle

Answer

A

Explanation

Here, `x=2 sin omegat :. (x)/(2)=sin omegat`
`y=2sin (omegat+(pi)/(4))`
`:. (y)/(2)=sin omegat cos ((pi)/(4))+cosomegat sin((pi)/(4))`
`(y)/(2)=((x)/(2))((1)/(sqrt(2)))+sqrt(1-(x^(2))/(4))xx(1)/(sqrt(2))`
Squaring both sides, we shall get a relation which represents an ellipse