Abstract: The response reachable set is defined for a linear time invariant vibration system excitation of which is modeled by a convex set. The problem of resolving the convex responses of MDOF vibration system is transformed into that of finding the response reachable set. A support hyperplane method of finding the response reachable set to the excitation modeled by aspecial convex set is presented. An analytical expression is obtained for the boundary point of the finite time response reachable set at a directio...