Application of finite integral transformation method to the solution of a mixed problem with integral condition of vibration process

In the present paper, using the finite integral transformation method, we obtain analytic representation of classic solution of mixed problems with integral condition of vibrations process, described by a wave equation and running its course for period of time 0 ≤ t ≤ T. It is assumed that points with coordinates x = 0 and x = 1 are the ends of the vibrating string