A system with input r(t) and output y(t) is given by the following differential equation dy(t)...

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A system with input r(t) and output y(t) is given by the following differential equation d²y(t) dt² +2 dy(t) dt + y(t) = x(t). Assume initial rest, that is, y(-x) = 0 and dy(t)/dt = 0. Also assume that the system is causal. Find the impulse response of this system. Next, find the output of this system when input is cos(xt). It=-∞ A system with input r(t) and output y(t) is given by the following differential equation d²y(t) dt² +2 dy(t) dt + y(t) = x(t). Assume initial rest, that is, y(-x) = 0 and dy(t)/dt = 0. Also assume that the system is causal. Find the impulse response of this system. Next, find the output of this system when input is cos(xt). It=-∞

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