44. A causal LTI system has zero initial conditions and impulses response h(t). Its input x(t) and output y(t) are related through the linear constant-coefficient differential equation

\({d^2y(t)\over dt^2}+a{dy(t)\over dt}+a^2y(t)=x(t)\)

Let another signal g(t) be defined as

\(g(t)=a^2\int^t_0h(\tau)d\tau+{dh(t)\over dt}+ah(t)\)

If G(s) is the Laplace transform of g(t), then the number of poles of G(s) is _______.

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