Out-of-phase solutions to a second order linear differential equation with forced oscillation

A criterion is developed to determine the existence of an out-of-phase solution to a second order linear equation with an oscillatory forcing function. Although the general criterion is difficult to check, if a solution can be exhibited that has zeros at the zeros of the forcing function and the associated homogeneous equation is disconjugate, then the solution must be out-of-phase. In addition, a general class of examples is given which can be used to obtain easily verifiable criteria for specific examples.