This animate command shouldn't ignore the options to show() that are passed through by the plot command (here the options are ymin and ymax):
sage: var('t')
sage: damped_oscillator = 41/311*sqrt(311)*e^(-3/8*t)*sin(1/8*sqrt(311)*t) + 3*e^(-3/8*t)*cos(1/8*sqrt(311)*t)
sage: animate([plot( lambda x: damped_oscillator( t = x + k ), -1/2, 3*pi, ymin=-2, ymax=3.5 ) for k in srange( 0, pi, 0.3 ) ]).show()
 
Thanks to Johann Myrkraverk Oskarsson for reporting this.
CC:  @sagetrac-wcauchois
Component: graphics
Author: Jason Grout, Andrey Novoseltsev
Reviewer: Tim Dumol, Marshall Hampton, Karl-Dieter Crisman
Merged: sage-4.6.2.alpha2
Issue created by migration from https://trac.sagemath.org/ticket/7981