Question

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:
A. an ellipse
B. a straight line
C. a parabola
D. circle

Answer 1

Correct Answer - A
Hence `simomegat=(x)/(2)`
`cosomegat=(sqrt(4-x^2))/(2)`
`y=2sinomegat+(2)/(sqrt2)cosomega` ltbgt `=sqrt2xx(x)/(2)+sqrt2(sqrt(4-x^2))/(2)`
`=(x)/(sqrt2)+(sqrt(4-x^2)/(sqrt2))`
or `sqrt2y-x=sqrt(4-x^2)`
or `2y^2+x^2-xy=4-x^2`
or `2y^2+2x^2-xy=4`
or `x^2+y^2-sqrt2xy=2`
This is an equation of ellipse.