A particle of mass m can slide freely along a wire AB whose perpendicular distance to the origin O is h The line OC rotates about the origin at a constant angular velocity theta w The position of the particle can be described in terms of the angle theta and the distance q to the point C If the part...

mg Using 9 and 8 t since 8 0 0 the xy coordinates of the particle are expressed as x h cos 0 q sin 0 ...

A particle of mass m can slide freely along a wire AB whose perpendicular distance to the

Question:

A particle of mass m can slide freely along a wire AB whose perpendicular distance to the origin O is h. The line OC rotates about the origin at a constant angular velocity θ = w. The position of the particle can be described in terms of the angle θ and the distance q to the point C. If the particle is subject to a gravitational force, and if the initial conditions are θ(0) = 0, q (0) = 0, q(0) = 0 show that the time dependence of the coordinate q is q/t = g/2w2 (cosh wt €“ cos wt) Sketch this result. Compute the Hamiltonian for the system, and compare with the total energy. Is the total energy conserved?

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