2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/213451We present analytical results on the propagation of a classical string in non-zero modes through the singularity of the compactified Milne space. We restrict our analysis to a string winding around the compact dimension of spacetime. The compact dimension undergoes contraction to a point followed by re-expansion. We demonstrate that the classical dynamics of the string in excited states is non-singular in the entire spacetime.Version accepted for publication in Class. Quantum GravGeneral Relativity and Quantum Cosmologytext