Solution of a Boundary Value Problem on Semi-Bounded String Motion with the Boundary Condition of the Third Kind
He paper considers the boundary problem of motion of semi-bounded string with the free end operated by an elastic force, which is proportional to the displacement of the spring type. With the help of the method of convolution of Fourier expansions, solution of the problem is expressed in explicit form by means of the classical Cauchy problem solution for an unbounded string. In limiting cases, the obtained solutions result in the solutions of classical problems for semi-bounded strings with a free and a ﬁxed end point.