  We study earthquake deformations on Teichm\"uller space associated with
simple closed curves of the once-punctured torus. We describe two methods to
get an explicit form of the earthquake deformation for any simple closed curve.
The first method is rooted in linear recurrence relations, the second in
hyperbolic geometry. The two methods align, providing both an algebraic and
geometric interpretation of the earthquake deformations. We convert the
expressions to other coordinate systems for Teichm\"uller space to examine
earthquake deformations further. Two families of curves are used as examples.
Examining the limiting behaviour of each gives insight into earthquakes about
measured geodesic laminations, of which simple closed curves are a special
case.
