On a method of analytical solution of wave equation describing the oscillations sistem with moving boundaries

The method of analytical solution of wave equation with the conditions, assigned on the moving boundaries, is described. With the aid of the change of variables in the system of functional equations the original boundary-value problem is brought to the system of difference equations with one fixed bias, which can be solved using the Laplace integral transform. The expression for amplitude of oscillation corresponding to $n$-th dynamic mode is obtained for the first kind boundary conditions. This method makes it possible to examine the broader class of boundary conditions in comparison with other exact methods of solving the boundary-value problems with the moving boundaries.