Approximation of exponential sums in the problem on the oscillator motion caused by pushes

The application of the Hardy-Littlewood-Vinogradov-Van der Corput theorem on the approximation of exponential sums by shorter ones to the solution of the problem on quasiperiodic pushes acting on harmonic oscillator is considered. New asymptotic formulas for the solution of the problem for the pushes of various forms in the presence and in the absence of friction are obtained.