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A puck, a spring and a Coriolis force

### What is this?

A puck is attached to a spring that has
a natural length of zero. One end of the spring is
attached to the surface. Without a Coriolis force,
the angular frequency would be ω. A dimensionless
time is defined to as τ=ωt. The unit for distance
is taken to be the initial length of the spring.
The puck experiences a viscous drag force proportional to its
velocity. The components of the equation of motion
for the puck are:
dU/dτ= -X -αU + βV

dV/dτ= -Y -αV - βU

The initial conditions are X=1 and Y=0 and the puck
is motionless.

Here is something to try. Consider various values of
β, say ranging from 0.2 to 4, and take α=0.
Note the puck does not enter a "forbidden" circle around
the origin. For higher values of β, the forbidden circle is
larger.
Can derive an analytical expression for the
radius of the circle? Also note that for larger values of β
that the kinetic energy remains small and most of the
potential energy is never converted to potential energy.