Chapter 1

Resources and learning aids from the web

Section 1.1

Waves Syllabus Song”—a delightful song about the topics covered in this book.

Section 1.2

Biography of Robert Hooke
(Be aware that this is written by a big fan of Hooke, and so casts him in the most positive light possible.)

Hooke’s microscope (Image from Micrographia, by Robert Hooke, 1665)

Hooke and Newton Song”—short, sweet, and with whistling)

Physical Review Focus article on Hooke’s Law and the physics of rubber bands
(highlighting research done in 2007)

Section 1.3

Interactive quiz on the contents of section 1.3
Can you complete it within the time limit? Try as often as you like. Note: The first page has spaces to enter your name and e-mail address. Please leave these blank on your first try. If you feel ready to complete the quiz in less than 2 minutes, and would like to receive an official certificate of completion, then fill them in. If you earn enough certificates, then you will get a prize!

Inset image of sine waves © Stephen Gibson |

Section 1.4

Applet demonstrating the behavior of a mass on a spring.
(There is a small bug in the applet. To make it behave correctly, use your mouse to move the mass at least slightly before clicking on “Start”. The author of this applet is unknown.)

Section 1.5

Animation developed for this text showing the isomorphism between mechanical and electrical oscillators.

Section 1.6

A nice interactive applet on Taylor series by Prof. Daniel J. Heath.

Section 1.7

Euler’s equation is . Plugging in and rearranging gives , which is sometimes called Euler’s identity. This has been called the most beautiful equation in mathematics, partly because it relates e, i, and π. This elegant music video below by YouTube user VeritySeeker makes the case for this claim.

Section 1.8

History of complex numbers, from the University of Alberta.
Cover of “L’Algebra” by Rafael Bombelli, the “father of complex numbers”.

Animation by Dan Russell showing the relation between the rotating complex plane vector z(t) and its real part x(t).
(Note: Browsers don’t always play animated gifs properly, so you may have to download the image (by right-clicking and choosing “Save Target As”, then open it in a different program.)

Section 1.10

Paul Falstad has written a remarkable series of applets about physics and math, including a beautiful series of applets about circuits. It is best to start with this applet about resistors, to get used to the color scheme. I suggest that you don't change the controls for “Simulation Speed” or “Current Speed”. Green indicates positive voltage, grey indicates ground, and the yellow dots show the flow of current. Here’s a challenge: when you close the switch on the lower right, the current speeds up. (This should make sense.) Why does the current in the 200 Ω resistor stop flowing?

Another one by Paul Falstad: This applet shows the current flow in a capacitor that is charging or discharging, depending on the way you set the switch. Green shows positive voltage, red shows negative voltage, and grey shows ground. Again, I suggest that you don’t change the controls for “Simulation Speed” or “Current Speed”.

Paul Falstad’s applet showing current flows in an inductor. Depending on the way you set the switch, the current either starts up from zero or slows down from a starting value. As usual, I suggest that you don’t change the controls for “Simulation Speed” or “Current Speed”.

This series of five applets by Paul Falstad shows first the dependence of current on capacitance, then on frequency (for fixed capacitance), then on inductance, then on frequency (for fixed inductance), then on type of impedance (resistor, capacitor, or inductor). As usual, I suggest that you don’t change the controls for “Simulation Speed” or “Current Speed”. To move to the next applet in the series of five, click on the “Next” link under the applet.

This series of four applets by Paul Falstad encourages you to explore RC and RL filters. To start the action going, click on the graph at the bottom of the applet; this sets the frequency of the input waveform. You can also adjust the spectrum width and the “cutoff frequency” (i.e. the quantity 2π/RC), but as usual I think it’s best not to change the Simulation Speed or Current Speed. To move to the next applet in the series of four, click on the “Next” link under the applet.

Section 1.12

Physical Review Focus article on a recent experiment in which the Casimir effect was detected at the nanoscale.
A 196 μm diameter sphere (polystyrene coated with aluminum) mounted on a cantilever. Deflections of the cantilever were used to measure the Casimir force between the sphere and a flat surface. Reprinted figure with permission from U. Mohideen and A. Roy, Phys. Rev. Lett. 81, 4549–4552 (1998) . Copyright 1998 by the American Physical Society.

Notice for links to Physical Review Focus articles:
Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.

Website Terms and Conditions and Privacy Policy
Please send comments or suggestions about this Website to