@Rouben Rostamian Thank you greatly for the lesson on elasticity.
I was prompted to ask this question by the book "200 More Puzzling Physics Problems" by Gnadig, Honyek and Vigh, problem 61, which describes a Slinky anchored at a point in a horizontal tube which rotates horizontally about one end at a fixed angular velocity.
The book provides the following ODE solution:
diff(r(m),t,t) = -omega*sqrt(M/k)*r(m).
M is the mass of the Slinky, k is its spring constant, omega is the tube's angular velocity, and r is the length from the tube's rotation axis to any point on the Slinky as a function of the Slinky's mass within this length.
I would like to animate the Slinky as the tube containing it rotates but I don't know how to obtain the value of m which itself is a function of r. Can you refer me to a source which describes a mathematically accurate profile of a Slinky in this scenario?