The motion of a material point on a straight under the action of a nonlinear reconstructing force, friction, and a periodic external force, was studied. The point under consideration was assumed to experience absolutely elastic impacts against a fixed limiter. The proof of relevant applied theorem is based on the concept of overtaking principle. The overtaking phenomenon is a characteristic feature of impact systems and the maximum interval between neighboring moments of impact tends to zero. The obtained theorem were found valid for any period function h(t) with finitely many simple roots per period.