The Laplace transform is used to introduce initial conditions into the equations of motion of a linear chain ofNequal masses connected by equivalent springs. A concrete solution requires inversion of anN×Nmatrix and inversion of the Laplace transform. A recursive relationship is derived which allows the inverse matrix forNmasses to be easily obtained from the matrix forN−1 masses, and the inverse Laplace transform is obtained by the method of partial fractions. A general expression for certain partial fraction coefficients is derived, which makes it possible to determine the motion of the end mass of a semi‐infinite chain when this mass receives an impulse.