Sarthaks Test
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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.

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1 Answer

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

dv/dt = = -ω2r; F = -mω2r

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

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