2017-Morin, David - Oscillations - Notes

By Brian Winkel


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Morin, David. Oscillations. http://www.people.fas.harvard.edu/~djmorin/waves/oscillations.pdf . Accessed 11 September 2017. Notes. 37 pp.

From the first page

“A wave is a correlated collection of oscillations. For example, in a transverse wave traveling along a string, each point in the string oscillates back and forth in the transverse direction (not along the direction of the string). In sound waves, each air molecule oscillates back and forth in the longitudinal direction (the direction in which the sound is traveling). The molecules don’t have any net motion in the direction of the sound propagation. In water waves, each water molecule also undergoes oscillatory motion, and again, there is no overall net motion.1 So needless to say, an understanding of oscillations is required for an understanding of waves.

“The outline of this chapter is as follows. In Section 1.1 we discuss simple harmonic motion, that is, motioned governed by a Hooke’s law force, where the restoring force is proportional to the (negative of the) displacement. We discuss various ways to solve for the position x(t), and we give a number of examples of such motion. In Section 1.2 we discuss damped harmonic motion, where the damping force is proportional to the velocity, which is a realistic damping force for a body moving through a fluid. We will find that there are three basic types of damped harmonic motion. In Section 1.3 we discuss damped and driven harmonic motion, where the driving force takes a sinusoidal form. (When we get to Fourier analysis, we will see why this is actually a very general type of force to consider.) We present three different methods of solving for the position x(t). In the special case where the driving frequency equals the natural frequency of the spring, the amplitude becomes large. This is called resonance, and we will discuss various examples.”

This is a very good treatment with great analysis of harmonic oscillations, resonance, beats, frequency response, solution techniques, equilibrium, interpretation of terms and solutions, damping, over and under damping, with very appropriate graphics.

Keywords: differential equation, model, oscillation, harmonic oscillators, resonance, beats, frequency response, solution. techniques, equilibrium, damping, over damping, critical damping,  under damping

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Researchers should cite this work as follows:

  • Brian Winkel (2017), "2017-Morin, David - Oscillations - Notes," https://www.simiode.org/resources/4119.

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