A system has the transfer function(a) Find the system modes. These modes are not real, eve...

A system has the transfer function

(a) Find the system modes. These modes are not real, even though the system is a model of a physical system.

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(b) Express the natural response as the sum of the modes of Part (a) and as a real function.

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(c) The input e–t u(t) is applied to the system, which is initially at rest (zero initial conditions). Find an expression for the system output.

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(d) Show that the result in Part (c) satisfies the system differential equation and the initial conditions.

Suppose that the following differential equations are models of physical systems. Find the modes for each system. Is the system stable?

(b)