Chapter 27, Problem 25P

Derive the set of differential equations for a three mass–four spring system (Fig. P27.25) that describes their time motion. Write the three differential equations in matrix form,

$\left[\text{Acceleration <x-custom-btb-me data-me-id="1725" class="microExplainerHighlight">vector</x-custom-btb-me>}\right]+\left[k/m\text{ matrix}\right]\left[\text{displacement vector }x\right]=\text{0}$

Note each equation has been divided by the mass. Solve for the eigenvalues and natural frequencies for the following values of mass and spring constants: $k_1=k_4=15\text{ N/m, }{k}_2=k_3=35\text{ N/m, and }{m}_1=m_2=m_3=\text{1}\text{.5kg}\text{.}$