The inversion mechanism of a T-shaped Ar 3 is studied both classically and quantum mechanically. Regular states, localized in the region of the transition state for the inversion of the axial argon atom are found and are assigned by the symmetric stretch stable periodic orbits which emanate from the saddle point of the potential. These states inhibit the inversion process. States which promote the inversion are mainly irregular, but a few of them are localized and they have their nodes perpendicularly arranged along periodic orbits which originate from saddle node bifurcations. The two types of periodic orbits, inhibiting and isomerizing, are used to produce distinctly different spectra and to extract the corresponding eigenfunctions by solving the time dependent Schrödinger equation using a variable order finite difference method ͓J. Chem. Phys. 111, 10827 ͑1999͒, preceding paper͔.

The simple harmonic motion (SHM) is the simplest type of oscillatory motion. It is a key topic in most High School Physics curriculum with a rather demanding mathematical background for the students. A quite common approach for a better understanding of the motion is to visualize SHM as a projection of a uniform circular motion onto one axis. In this paper, we propose an experimental layout, which uses a specially designed object executing a uniform circular motion, in order to demonstrate the relationship between the changes in value and orientation of both the velocity and the acceleration vectors of its shadow that performs SHM. This idea was originally introduced in the second quarter of the 20th century and nowadays we combine it with the modern possibilities offered by 3D printing technology.

The interference pattern between two harmonic oscillations with slightly different frequencies are called beats. The beats, as a combined motion, have two different periods, one approximately equal to the period of the original oscillations, and another that is significantly longer and is related to the variable amplitude of the motion. The main objective of this presented work is to engage students’ attention and demonstrate in a simple way the concept of mechanical beats as a resultant motion of combined oscillations, but also to experience it through a visual projection. The proposed experimental setup is constructed in a way that satisfies both objectives and it consists of two parts that allow us to demonstrate in real time the combination of two harmonic motions. In the first part, the resultant motion is generated by the oscillations of two parallel rulers equipped with mirrors, and in the second part the visual demonstration of the beat occurs on a phosphorescent rotating foil by using a blue violet laser beam.