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In this paper, we analyze the motion of a falling Slinky, starting from rest and initially suspended from one of its ends. It is well-known that under these conditions, the Slinky moves in an unusual way: its lower end remains at rest until the upper end collides with it - as if gravity were being challenged! We conducted a literature review and identified that the most widely disseminated explanation for this levitation phenomenon of the Slinky's base during the Slinky's fall relies on the concept of information (and does not seem to please many). We show that such a phenomenon can be explained - and reproduced through a computer simulation using a simple model - without the notion that "there is a finite time for the information that the Slinky was released at its top to reach its bottom". [ABSTRACT FROM AUTHOR]

In this paper we introduce Schrödinger's operators in a naive and unpretentious way, but with some precision and didactics. The most studied periodic and random potential types are mentioned and, by numerical simulation, compare the eigenvalues of an operator's truncated matrix with a periodic potential and the same potential disturbed by an evenly distributed continuous random variable. We evaluated the magnitude of the random variable required to produce a significant difference between the eigenvalue sets. [ABSTRACT FROM AUTHOR]

We have recently developed a software to simulate a given physical phenomenon, without the need of knowing its corresponding equation of motion. This procedure is actually intended to illustrate the behavior of dynamical variables of interest, such as position, velocity, acceleration and energy. In our work, we present analytical solutions for each case under consideration; numerical solutions carried out by means of the finite difference method are presented as well. The harmonic oscillator is a moving periodical system, with a well-defined equilibrium position. We shall here present an overview of the general problem to be solved and a number of special cases shall be worked out in details. As one of the purposes of this article is to encourage readers to use numerical approaches to inspect physical problems, we shall discuss in a simple and direct way the numerical solutions of a mechanical oscillator. We also contemplate the behavior of the energy function and point out under which particular situations it is conserved. To validate the numerical method implemented in our paper, we compare the analytical solutions we derive with the results obtained by numerical computations. [ABSTRACT FROM AUTHOR]