Question: Consider the homogeneous input-output differential equation (Input-Output model), [begin{align*}ddot{y}+y & =0 tag{3.24}text { where } y(0) & =alpha text { and } dot{y}(0)=beta .end{align*}] (a)

Consider the homogeneous input-output differential equation (Input-Output model),

\[\begin{align*}\ddot{y}+y & =0 \tag{3.24}\\\text { where } y(0) & =\alpha \text { and } \dot{y}(0)=\beta .\end{align*}\]

(a) Find the system response \(y(t)\).

(b) How can this response be verified?

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