Chapter 8.7, Problem 58E

(a)

To determine

To show: The given system of equation can be written in matrix form $M{x}^{″}=Kx$.

(b)

To determine

To show: The matrix form $M{x}^{″}=Kx$ can be written as ${\text{x}}^{″}=\text{Ax}$.

(c)

To determine

To show: The expression $X\left(t\right)=\text{v}{e}^{\alpha t}$ satisfies the system if and only if ${\alpha }^2=\text{λ}$ for the given condition.

(d)

To determine

To show: The two solution of $X\left(t\right)=\text{v}{e}^{\alpha t}$ is $X_1=v\cos \omega t$ and $X_2=v\sin \omega t$ for the given condition.