Chapter 6.4, Problem 14P

Consider the two-mass, three-spring system whose equations of motion are Eqs.(11) in text. Let $m_1=m_2=m$ and $k_1=k_2=k_3=k$. Find the general solution in terms of the parameter $\omega =\sqrt{k/m}$. In terms of $\omega$, what are the principal modes of vibration and the corresponding natural frequencies?