{"paper":{"title":"Hypergeometric solutions to a three dimensional dissipative oscillator driven by aperiodic forces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alessio Bocci, Daniele Ritelli, Giovanni Mingari Scarpello","submitted_at":"2016-12-13T16:02:39Z","abstract_excerpt":"We model the dynamical behavior of a three dimensional (3-D) dissipative oscillator consisting of a $m$-block whose vertical fall occurs against a spring and which can also slide horizontally on a rigid truss rotating at a known angular speed law $\\omega(t)$. The $z$-vertical time law is obvious, whilst its $x$-motion along the horizontal arm is ruled by a linear differential equation to be solved through the Hermite functions and the Confluent Hypergeometric Function (CHF) $_{1}F_{1}$ (Kummer). After the rotation time law $\\theta(t)$ has been computed, we know completely the mass motion in a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04253","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}