<p>The problem of oscillation of a pendulum on a flexible, stretchable string is investigated. We consider the motion of a gravitational pendulum on an elastic string in which transverse and longitudinal oscillations can occur. The equations of motion are coupled nonlinear hyperbolic partial differential equations. An analytical asymptotic method for solving this nonlinear problem is proposed, which allows separating low-frequency and high-frequency movements occurring in the problem. The asymptotic method allows to obtain a hyperbolic system of equations for the high-frequency approximation and an elliptic system for the low-frequency approximation, the solutions of which can be found in asymptotic series. The influence of longitudinal and transverse vibrations of the string is investigated. Corrections to the frequency of the swinging spring are found which occur if the wave processes are taken into account. The transfer of energy from the longitudinal vibrations of the mass to the transverse vibrations of the string is revealed. For certain values of the initial parameters the amplitude of the transverse vibrations of the string can increase several times, the lower the tension the greater the amplitude of the transverse vibrations of the string. The proposed numerical method shows a good correspondence with analytical solutions. The experiments confirm the presence of energy transfer from longitudinal and transverse vibrations.</p>