A bead of mass \(m\) is threaded without friction on a massless wire hoop of radius \(R\) that is forced to oscillate vertically in a fixed vertical plane at angular frequency \(\omega\) and with amplitude \(a\). Is the system holonomic? Construct a Hamiltonian for the system and obtain hamilton's equations. Does the system conserve energy? (Hint: Consider the external system.)

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a -R- a gravity bead