A puck, a spring and a Coriolis force

show spring?

show forces?





total accel.

spring accel.

viscous accel.

Coriolis accel.

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.