This paper deals with the forced vibrations described by the differential equation
wherein Φ denotes a nonlinear function of q and/or q̇. It presents a criterion for determining their stability. It is shown that under very weak restrictions, which equivalently means, for a large variety of cases (including all of practical importance) the stability depends on the sign of ∂q*/∂P (q* denoting the maximum value of q(t) within a period). The motion is stable if this derivative is positive; it is unstable if it is negative.
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