@Rouben Rostamian  Once again I am in your debt. Is it true for any two 3D surfaces which are tangent to each other that their normals at their common point of tangency are collinear?

@Rouben Rostamian  Thank you for taking the time to answer me. Since my math skills are about middle undergraduate this subject is interesting but far over my head.

@Carl Love When I execute the 4th method I receive "Error (in Last) too many levels of recursion".

The following code works in Maple 2016

Last := proc (k::posint)

procname(k) := 4*thisproc(k-1)+k :

end proc:

Last(0) := 1:

`seq`(Last(k), k = 1 .. 10);

@Christopher2222 are enlightening. It is fascinating that this question has drawn the interest of a number of early calculus stars.

@Rouben Rostamian  your reference and the animation. Christopher 2222's references are also interesting.

@Carl Love I am always happy to expand my understanding of Maple's myriad capabilities and appreciate your helping me to do so.

@vv You show an interesting alternative. Are there cases where command inequal is generally superior to (or inferior to) the implicitplotting of an inequality? 

@Kitonum You show that plotting the function lhs-rhs created from the inequality lhs>=rhs illustrates the logic of implicitplotting of the inequality. Thanks to you I now have a better understanding.

@Rouben Rostamian  Thank you as always.

Below is a worksheet which finds the values of all of its ODE's variables at the time of event firing.

Eventfired.mw

@Rouben Rostamian  I am delighted that you continue to be interested in my question and I appreciate your advice re improved programming.

Before tackling problem 61 I would have expected Slinky's loops to be further apart as centripetal force increases with distance from its fixed point, but the math doesn't lie.

It seems you already had the "200 More..." book in your library. It and its predecessor are an excellent source of physics challenges. I look forward to your help when I am stuck on future problems. 

@Rouben Rostamian  This is great! Your worksheet above has enabled me to display Slinky extended by the centrifugal force of rotation.

Please check the code I have added to yours in the worksheet below. I will appreciate any comments you care to make.

Slinky2.mw 

If the above is accurate, I will proceed to animate the rotation.

@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?

@Kitonum In my Maple2016 this procedure does not produce the above results and I can't find relevant help text.

Is there Maple2016 code that can produce these results? Is there help text explaining this interleave capability?

@tomleslie Thank you for your answer.

I recently found the technique below in one of Dr. Lopez's applications.

Please comment on its validity.

Efield_contours.mw

Sorry, I forgot to eliminate the reference to my document library.

@Rouben Rostamian  You have provided me with many answers and I am grateful for each of them.

I will take the time to digest your worksheet and communicate any questions which arise.

For your interest, my question is an expansion of problem 13 in "200 Puzzling Physics Problems" by Peter Gnadig, Gyula Honyek and Ken Riley, Cambridge University Press.