Two point masses, each of mass $m$, are constrained to lie on a straight line and are connected to each other by a spring of force constant $k$. The left-hand mass is also connected to a wall on the left by a spring of force constant $j$. The right-hand mass is similarly connected to a wall on the right, by a spring of force constant $\ell$, so that the potential energy is

$$V=\frac{1}{2} k\left(\eta_{1}-\eta_{2}\right)^{2}+\frac{1}{2} j \eta_{1}^{2}+\frac{1}{2} \ell \eta_{2}^{2}$$

where $\eta_{i}$ is the distance from equilibrium of the $i^{\text {th }}$mass. Derive the equations of motion. Find the frequencies of the normal modes.