InterviewSolution
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InterviewSolution
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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` . |
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Answer» Here (a) ` vec(r) (t) = hati A cos omegat + hatj B sin omegat, :. x = A cos omegat, y = B sin omegat ` ` x^(2)/(A^(2)) + y^(2)/(B^(2)) cos^(2) omegat + sin^(2) omegat = 1` which is the equation of an ellipse `:.` The trajectory of the particle is elliptical (b) Now ` vec(upsilon) =vec (dr)/(dt) = -hatiomega A sin omegat + hatjomega Bcos omegat ` ` 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) ` ` vec(F) = m vec (a) = - m omega^(2) vec(r) ` . |
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