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A glance at Bessel functions shows they behave similar to the damped sinusoidal function. In this paper two physical examples (pendulum and spring-mass system with linearly increasing length and mass respectively) have been used as evidence for this observation. It is shown in this paper how Bessel functions can be approximated by the damped sinusoidal function. The numerical method that is introduced works very well in adiabatic condition (slow change) or in small time (independent variable) intervals. The results are also compared with the Lagrange polynomial.

In one dimension, we investigate dynamics using special relativity only, but make no statement regarding any particular insight into the nature of the spacetime continuum. Indeed, we do away completely with any kind of formal tensor algebra or differential topology, but do incorporate scaling into our calculations. The purpose here is primarily pedagogical, as an extension to the standard undergraduate treatment of special relativity, but it is also a calculational tool, to be able to determine the motion of objects in a one-dimensional case even with accelerations and forces, without having to use the full general relativistic treatment. To illustrate this, we directly compare relativistic to Newtonian or non-relativistic motions for particularly instructive selected systems.

Projectile motion in classical physics can be defined as a two-dimensional motion with constant acceleration in one direction and uniform motion in another direction. In classical mechanics this motion can be achieved if a force is applied in one direction and with some initial velocity in another direction. In relativistic dynamics, the equations of motion in both directions are coupled to each other and surprisingly the object experiences varying accelerations in both directions. We can say the non-relativistic projectile motion is not a projectile motion at all in relativistic physics. In this paper the conditions for the projectile motion in the relativistic regime are discussed. We discuss the two cases of constant force and constant acceleration. Another goal of this paper is that to show a computational example can be discussed in class for students to learn a topic in physics and improve their computational skills.