Consider a linear system governed by the differential equation
m \ddot{x}(t) + c \dot{x}(t) = f(t)The accompanying sketch shows one physical system that is governed by this differential equation, with c being a dashpot value and f(t) the force applied to the mass m . Find the impulse function h_{x}(t) such that Eq. 5.2
x(t)=\int_{-\infty }^{\infty }{f(s)h_{x}(t-s)ds} \equiv \int_{-\infty }^{\infty }{f(t-r)h_{x}(r)dr}describes the solution of the problem.