A Slinky is a loose helical coil spring and is a well-known educational toy. In this paper a model for a Slinky is presented. The Slinky is represented as a sequence of rigid half coils connected by torsional springs. A range of Slinky configurations in static equilibrium are calculated. Where possible the torsion spring model is compared with the…

The cases of constant and quadratic damping of free oscillations are missing from standard textbooks, even at college and university level. The case most examined is that of linear damping, the reason being that the student can work out a closed form which describes all stages of motion. The case of constant damping is straightforward to be…

Mechanical engineering students often find the formulation and analysis of dynamical systems difficult. The response of some mechanical engineering undergraduates is that as much as possible courses on mechanics are best avoided. The aim of this paper is to produce some interesting dynamical systems that may help to change the opinions of the…

Use of three-force member concept for rigid bodies whenever possible, to circumvent the more taxing use of equilibrium equations has been long-established. However, most students fail to reap its benefits due to a number of reasons, including the fact that its importance is hardly emphasized to them; skills and details needed for the concept are…

We present the results of an experimental project, made at the University of Calabria, which uses computer simulations and scientific computational systems in teaching and learning the fundamentals of analytic mechanics, in particular the classical Lagrangian and Hamiltonian formulation of the matter. Starting with examples of classical dynamical…

It is well known that mechanical engineering students often find mechanics a difficult area to grasp. This article describes a system of equations describing the motion of a balanced and an unbalanced roller constrained by a pivot arm. A wide range of dynamics can be simulated with the model. The equations of motion are embedded in a graphical…

Viscous damping is commonly discussed in beginning differential equations and physics texts but dry friction or Coulomb friction is not despite dry friction being encountered in many physical applications. One reason for avoiding this topic is that the equations involve a jump discontinuity in the damping term. In this article, we adopt an energy…

This paper deals with the modern development of matrices, linear transformations, quadratic forms and their applications to geometry and mechanics, eigenvalues, eigenvectors and characteristic equations with applications. Included are the representations of real and complex numbers, and quaternions by matrices, and isomorphism in order to show…

In this note, a simple proof of the Generalized Ceva Theorem in plane geometry is presented. The approach is based on the principle of equilibrium in mechanics. (Contains 2 figures.)

Discusses reasons for and ways of using computer software to teach mechanics. Describes using software to explore mechanics, challenge misconceptions, make links between mathematical representations and motion, and solve non-standard problems. Stresses the need for structured approaches to the use of software. (Contains 24 references.) (Author/ASK)

This note presents and discusses a class of real integrals involving a hyperbolic function by means of complex integration. An integral representation is obtained which appears in several fields of physics, including statistical mechanics, condensed matter and quantum optics and more in the so called dispersion relations.

A gamut of mathematical subjects and concepts are taught within a handful of courses formally required of the typical engineering student who so often questions the relevancy of being bound to certain lower-division prerequisites. Basic classes at the undergraduate level, in this context, include: Integral and Differential Calculus, Differential…

The author advocates changing the traditional approach to mechanics from emphasis on the formulation of Newton's Laws to discussion of the foundations of mechanics and Mach's formulation. (SD)

Describes how to use the computer algebra system (CAS) Mathematica to analyze projectile motion with and without air resistance. These experiments result in several conjectures leading to theorems. (Contains 17 references.) (Author/ASK)