Abstract
In this chapter we examine oscillating systems. In particular, we focus on harmonic oscillations produced by linear forces. We begin by showing why such oscillations are common and then proceed to an analysis of oscillating systems with and without damping and driving forces. The chapter concludes with a brief examination of an oscillating system with nonlinear forces, namely the simple pendulum.
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Notes
- 1.
The commands, essentially identical to those above, are omitted.
- 2.
The commands, essentially the same as those used to generate Fig. 4.12, are omitted.
- 3.
The steady state portion of the solution, which is the part we are most interested in, is the same whether the oscillator is underdamped, overdamped, or critically damped.
- 4.
The commands, essentially the same as those used to produce 4.22, are omitted.
- 5.
The Symbol commands might not work in all Maxima installations. The text entries theta and omega may be substituted.
- 6.
Unless the option draw_realpart=false is used the graph will show horizontal lines at ω = 0. This happens because, by default, draw plots the real part of complex-valued functions. We use the command set_draw_defaults at the beginning of the workbook to suppress the drawing of the real parts of complex values and well as to set other default values.
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© 2016 Todd Keene Timberlake & J. Wilson Mixon, Jr.
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Timberlake, T.K., Mixon, J.W. (2016). Oscillations. In: Classical Mechanics with Maxima. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3207-8_4
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DOI: https://doi.org/10.1007/978-1-4939-3207-8_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-3206-1
Online ISBN: 978-1-4939-3207-8
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