Past exam of the mathematical methods II course of the University of Oxford / 2016 / 9 / a / Solution

Each spring force is its extension multiplied by the spring constant, acting to restore the equilibrium. The equations of motion areNo end is attached to a wall. The spring extensions are $x_2-x_1$ and $x_3-x_2$, giving potential energy $k[(x_2-x_1{)}^2+(x_3-x_2{)}^2]/2$.