Exact and closed-form solutions are obtained for both tangential and vertical surface displacements of a homogeneous isotropic elastic half-space due to the application, at a point on the surface, of a concentrated force tangential to the plane boundary and varying with tine as the Heavyset unit function. Similar expressions for the displacements in the interior of the body alone a line directly below the applied force are derived. Solutions are obtained by a semi-inverse method with the aid of lap lace and Hankie transforms. Combination of these solutions with those given earlier by Iamb and Fakeries, which give the surface displacements due to the application of a normal time-dependent force, will give the response to any in¬clined time-dependent force applied on the plane boundary. The reciprocal relation in the static case, between tangential surface displacement due to a vertical force and vertical surface displace¬ment due to a tangential force applied on the plane boundary is preserved in the dynamic case.
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