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We model the dynamical behavior of a three dimensional (3-D) dissipativeoscillator consisting of a $m$-block whose vertical fall occurs against aspring and which can also slide horizontally on a rigid truss rotating at aknown angular speed law $\omega(t)$. The $z$-vertical time law is obvious,whilst its $x$-motion along the horizontal arm is ruled by a lineardifferential equation to be solved through the Hermite functions and theConfluent Hypergeometric Function (CHF) $_{1}F_{1}$ (Kummer). After therotation time law $\theta(t)$ has been computed, we know completely the massmotion in a cylindrical coordinate reference: some transients have then beendiscussed. Finally, further effects as an inclined slide and a contact dryfriction have been added to the problem, so that the motion differentialequation becomes inhomogeneous and we resort to Lagrange method of variation ofconstants, helped by a Fourier-Bessel expansion, in order to manage therelevant intractable integrations.

Hypergeometric solutions to a three dimensional dissipative oscillator driven by aperiodic forces