Past exam of the mathematical methods II course of the University of Oxford / 2013 resit / 9 / a

Take laboratory displacements from the equilibrium positions with the support at $f=0$. The left spring's dynamic extension is $x_1-f(t)$ and the spring between the masses has dynamic extension $x_2-x_1$. Hooke's law and Newton's second law giveEquivalently,The natural length sets the equilibrium separations but disappears from these displacement equations. The support is externally prescribed, so no additional support equation is required.