Two linear simple harmoic motions of equal amplitude and frequencies omega and 2omega are impressed on a particle along the axes of x and y respectively . If the initial phase difference between them is pi//2 , find the resultant path followed by the particles.

Two linear simple harmoic motions of equal amplitude and frequencies o

1.	Two linear simple harmoic motions of equal amplitude and frequencies omega and 2omega are impressed on a particle along the axes of x and y respectively . If the initial phase difference between them is pi//2 , find the resultant path followed by the particles.
Answer» Solution :We have , x= A cos `OMEGA t , y = A cos (2OMEGA t + pi//2) = - A sin 2 omega t ` `=- A (2sin omega t cos omega t ) = - 2Asqrt(1-(x^2)/(A^2)) x/A =-2xsqrt(1-(x^2)/(A^2)) ` or `y^2 = 6x^2 (1-(x^2)/(A^2))`