The displacement vector of a 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 = - m omega^(2) r .

The displacement vector of a mass m is given by r (t) = hati A cos ome

1.	The displacement vector of a 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 = - m omega^(2) r .
Answer» <html><body><p></p>Solution :Here (a) ` vec(r) (t) = <a href="https://interviewquestions.tuteehub.com/tag/hati-2693493" style="font-weight:bold;" target="_blank" title="Click to know more about HATI">HATI</a> A cos omegat + hatj B sin omegat, :. x = A cos omegat, y = B sin omegat ` <br/> ` x^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)/(A^(2)) + y^(2)/(B^(2)) cos^(2) omegat + sin^(2) omegat = <a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>` which is the equation of an <a href="https://interviewquestions.tuteehub.com/tag/ellipse-450431" style="font-weight:bold;" target="_blank" title="Click to know more about ELLIPSE">ELLIPSE</a> <br/> `:.` The trajectory of the particle is elliptical <br/> (b) Now ` vec(upsilon) =vec(dr)/(dt) = -hatiomega A sin omegat + hatjomega Bcos omegat ` <br/> ` vec(a) = vec (d upsilon)/(dt) = hati omega^(2) A cos omegat - hatj omega^(2) B sin omegat = - omega^(2) [hati A cos omegat + hatjBsin omegat] = - omega^(2) vec(r) ` <br/> ` vec(F) = m vec (a) = - m omega^(2) vec(r) ` .</body></html>