Lissajous figures are parametric equations that deconstruct into equations of simple harmonic motion. They were a source of inspiration by artists and mathematicians alike, well before the digital age, due to their esthetic forms and simple equations that could be easily deconstructed. Here for the first time in literature, we present Lissajous…

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…

This paper gives the solution and analysis of projectile motion in a vacuum if the launch and impact heights are not equal. Formulas for the maximum horizontal range and the corresponding angle are derived. An Excel application that simulates the motion is also presented, and the result of an experiment in which 38 secondary school students…

We describe an example of learning with multiple representations in an A-level revision lesson on mechanics. The context of the problem involved the motion of a ball thrown vertically upwards in air and studying how the associated physical quantities changed during its flight. Different groups of students were assigned to look at the ball's motion…

In the teaching of physics at upper secondary school level (K10-K12), the students are generally taught to solve problems analytically, i.e. using the dynamics describing a system (typically in the form of differential equations) to compute its evolution in time, e.g. the motion of a body along a straight line or in a plane. This reduces the scope…

We describe a simple dynamical model of a one-dimensional ideal gas and use computer simulations of the model to illustrate two fundamental results of kinetic theory: the Boltzmann transport equation and the Boltzmann "H"-theorem. Although the model is time-reversal invariant, both results predict that the behaviour of the gas is time-asymmetric.…

Modelling elastic filament dynamics is a topic of high interest due to the wide range of applications. However, it has reached a high level of complexity in the literature, making it unaccessible to a beginner. In this paper we explain the main steps involved in the computational modelling of the dynamics of an elastic filament. We first derive…

A technique discovered in 1939 can be used to build a device that is driven by standard circular motion (as in a drill press) and drills exact square holes. This device is quite different from the classic design by Watts, which uses a Reuleaux triangle and drills a hole that is almost, but not exactly, square. We describe the device in detail,…

This paper addresses the difficulties experienced by first-grade students studying rigid body motion at Sofia University. Most quantities describing the rigid body are in relations that the students find hard to visualize and understand. They also lose the notion of cause-result relations between vector quantities, such as the relation between…

A three-dimensional pendulum, modelled after the Laser Interferometer Gravitational-Wave Observatory's suspended optics, was constructed to investigate the pendulum's dynamics due to suspension point motion. In particular, we were interested in studying the pendular-pitch energy coupling. Determination of the pendular's Q value (the quality factor…