Find the trajectory equation `y(x)` of a point if it moves according to the following laws `:`
`(a)` `x=a sin omega t, y= a sin 2 omega t,`
`(b)` `x= a sin omega t , y=a cos 2 omega t. `

Explanation

From the Eqn. `: x=a sini omegat , ` we have
`cos omega t=sqrt(1-(x^(2)//a^(2)))`
and from the Eqn. `: y=a sin 2 omegat `
`y=2a sin omega t cos omegat =2 x sqrt(1-(x^(2)//a^(2)))` or `y^(2)=4x^(2)(1-(x^(2))/(a^(2)))`
(b) From the Eqn. `: x = a sin omegat t ,`
`sin^(2) omega t = x^(2)//a^(2)`
From `y=a cos 2 omega t`
`y=a (1-2 sin ^(2) omegat)=a (1-2 (x^(2))/(a^(2)))`
For the plots see the plots of answer sheet of the problem book.