Question

The displacement vector of a particle of mass m is given by r(t ) = cap i A cos ωt + cap j Bsin ωt. 

(a) Show that the trajectory is an ellipse. 

(b) Show that F = −mω²r.

Answer 1

dr/dt = v = - cap i ωA sin ωt + cap j ωB cosωt

dv/dt = a = -ω²r; F = -mω²r

x = A cos ωt, y = B sin ωt ⇒ x²/A² + y²/B² = 1