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Question 5.2: Consider a linear system governed by the differential equati...

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.

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