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

The displacement vector of a particle of mass m is given by r(t) = hat

1.	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
Answer» Solution :Displacementvector`vec( r )= xhat(J )+ YHAT(j )` here `vec( r )= (ACOS t hat(j) ) = ( Bsinhat(I ))` Whichis equationof ellipse (b )velocityof theparticle `v= (DR )/( DT) = hat(I ) (d ) /(dt )+ hat(j ) (d ) /( dt ) ` Accelerationof theparticle(a ) ora= ` A (d ) /( d )(sinhat(j )+ B(d )/(dt ) coshat(j ))` `= [hat(j )cost + hat(j ) Bsint ]` forceactingon theparticle `f= ma=- m w^(2)r` Henceprove.