In this paper, we study the response to external disturbances of a double integrator with a saturating feedback. For a class of disturbances that have bounded integrals over all intervals, we show that a linear static feedback law can always be designed to ensure boundedness of the states. Moreover, boundedness can be preserved if the disturbance is biased by a small DC signal. In the special case that the disturbance is made up of a finite number of sinusoids and a small bias, any linear static feedback ensures boundedness of the states. These results are an extension of previous results by Wen, Roy, and Saberi (2008). (C) 2011 Elsevier Ltd. All rights reserved.