This paper describes a simple experiment that lets first-year physics and engineering students discover an important physical property of a Slinky. The restoring force for the fundamental oscillation frequency is provided only by those coils between the support and the Slinky center of mass.

The real power of calculus is revealed when it is applied to actual physical problems. In this paper, we present a calculus inspired physics experiment suitable for high school and undergraduate programs. A model for the theory of the terminal velocity of a falling body subject to a resistive force is developed and its validity tested in an…

Instead of solving ordinary differential equations (ODEs), the damped simple harmonic motion (SHM) is surveyed qualitatively from basic mechanics and quantitatively by the instrumentality of a graph of velocity against displacement. In this way, the condition b ? [square root]4mk for the occurrence of the non-oscillating critical damping and…

The wave equation with variable tension is a classic partial differential equation that can be used to describe the horizontal displacements of a vertical hanging chain with one end fixed and the other end free to move. Using a web camera and TRACKER software to record displacement data from a vibrating hanging chain, we verify a modified version…

We propose an analytic solution to the problem of the mechanical paradox consisting of a sphere rolling upwards on two diverging inclined guides as devised by Gardner. The presence of an unstable equilibrium point is highlighted and the analytic solution is found by means of elementary calculus concepts. (Contains 4 figures and 3 footnotes.)

A common example of real-world motion that can be modeled by a differential equation, and one easily understood by the student, is the simple pendulum. Simplifying assumptions are necessary for closed-form solutions to exist, and frequently there is little discussion of the impact if those assumptions are not met. This article presents a…

Provides diagrams and text to describe the procedures and results of an experiment used to introduce students to parametric resonance. (ZWH)