Abstract
This chapter is about ideas, concepts, and definitions that we will thoroughly use throughout this book. We will talk about periodic motions, including simple harmonic motion, wave motion, and orbital motion, with as less mathematics as possible. Most of this is high school stuff and the reader who is already familiar with the concepts may easily skip this.
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Notes
- 1.
An ideal simple pendulum, a mathematical abstraction, is a point mass hung by a massless thread that does not stretch under tension. A small spherical mass hung by an ordinary cotton thread is a very good approximation.
- 2.
That is, \(\omega \) is a real number.
- 3.
A sine function changes into a cosine function with a phase shift of \(90^\circ \), so we will club them together.
- 4.
\(\sin \theta \) can be expanded in an infinite series:
$$\begin{aligned} \sin \theta =\theta -\theta ^3/3! + \theta ^5/5! - ..{.} \end{aligned}$$so SHM means the \(\theta ^3\) term must be much smaller than \(\theta \). For \(\theta < 4^\circ \), the second term is less than \(0.1\%\) of the first term.
- 5.
Sometimes, scientists call all types of electromagnetic waves, be that radio waves, infrared, ultraviolet, X-rays, or \(\gamma \)-rays, light; the part that we can see is then called the visible light. This is a very narrow slice of the complete electromagnetic wave spectrum. See the Glossary for more on this.
- 6.
In the last decade of the last century, astronomers found something analogous to repulsive gravity in the very distant parts of the universe, where galaxies are accelerating away from each other. This has enigmatically been called the dark energy. No one yet knows what is behind the dark energy. However, this is not for us to discuss here.
- 7.
These are called absorption lines, as they appear when light is absorbed by atoms or ions. When sodium vapour is heated, you will see two bright D-lines exactly at the same position—they are behind the yellow colour of the sodium vapour lamp; such lines are known as emission lines. For any atom, absorption and emission lines occur exactly at the same position, the reason for which comes from the quantum mechanics and the model of atoms. How dark these lines appear depends on a number of factors, like the pressure, temperature, and concentration of that atom or ion. Indian astrophysicist Meghnad Saha (1893–1956) first showed how the composition of the star is related with the intensity of the spectral lines.
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Gangopadhyay, G., Kundu, A. (2024). On Periodic Motion. In: Rhythm in the Sky. Studies in Rhythm Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-97-2588-5_1
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DOI: https://doi.org/10.1007/978-981-97-2588-5_1
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