The displacement vector of a particle of mass m is given by r(t) = `hati A cos omegat + hatj B` sin `omegat`.
(a) Show that the trajectory is an ellipse.
(b) Show that `F= momega^(2)r`

Explanation

Displacement vector `vec( r ) = xhat(j ) + yhat(j )`
here `vec( r ) = (acos t hat(j ) ) = ( B sin hat(I ))`
Which is equation of ellipse
(b ) velocity of the particle
`v= (dr )/( dt) = hat(I ) (d ) /(dt ) + hat(j ) (d ) /( dt ) `
Acceleration of the particle (a )
or a= ` A (d ) /( d ) (sin hat(j ) + B (d )/(dt ) cos hat(j ))`
`= [hat(j ) cos t + hat(j ) B sin t ]`
force acting on the particle
`f= ma =- m w^(2) r ` Hence prove.