Through some fit continuation，the one -dimensional finite string vibrating problem with one end fixed and the other end doing forced vibration of Asin ωt is solved by the D'alembert formula. Based on the result expressed in a concise way，some variables to describe wave propagation are obtained and the process of the string vibration is analyzed. Furthermore，the problem of fixing solution with the first or second type boundary condition on one end and inhomogeneous boundary condition on other end is solved by using traveling wave method.