“A single particle is allowed to move between two fixed points. The springs both have spring constant $\kappa$. What is the differential equation that tells this atom what to do?”
This SWBQ will help gauge how familiar students are with describing classical harmonic oscillators (particularly through use of Hooke's Law) in terms of differential equations.
On the path to describing an arbitrary one-dimensional chain of atoms, this is one of the simplest cases that can be depicted. For students with less experience in differential equations, the wrap-up of this activity will also demonstrate that the D.E. describing a system is the key to finding the equation(s) of motion for that system.