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# 16: Oscillatory Motion and Waves


• 16.0: Prelude to Oscillatory Motion and Waves
• 16.1: Hooke’s Law - Stress and Strain Revisited
An oscillation is a back and forth motion of an object between two points of deformation. An oscillation may create a wave, which is a disturbance that propagates from where it was created. The simplest type of oscillations and waves are related to systems that can be described by Hooke’s law.
• 16.2: Period and Frequency in Oscillations
We define periodic motion to be a motion that repeats itself at regular time intervals, such as exhibited by the guitar string or by an object on a spring moving up and down. The time to complete one oscillation remains constant and is called the period. Its units are usually seconds, but may be any convenient unit of time.
• 16.3: Simple Harmonic Motion- A Special Periodic Motion
Simple Harmonic Motion (SHM) is the name given to oscillatory motion for a system where the net force can be described by Hooke’s law, and such a system is called a simple harmonic oscillator. If the net force can be described by Hooke’s law and there is no damping (by friction or other non-conservative forces), then a simple harmonic oscillator will oscillate with equal displacement on either side of the equilibrium position.
• 16.4: The Simple Pendulum
Pendulums are in common usage. Some have crucial uses, such as in clocks; some are for fun, such as a child’s swing; and some are just there, such as the sinker on a fishing line. For small displacements, a pendulum is a simple harmonic oscillator. A simple pendulum is defined to have an object that has a small mass, also known as the pendulum bob, which is suspended from a light wire or string.
• 16.5: Energy and the Simple Harmonic Oscillator
Energy in the simple harmonic oscillator is shared between elastic potential energy and kinetic energy, with the total being constant.
• 16.6: Uniform Circular Motion and Simple Harmonic Motion
If studied in sufficient depth, simple harmonic motion produced in this manner can give considerable insight into many aspects of oscillations and waves and is very useful mathematically. In our brief treatment, we shall indicate some of the major features of this relationship and how they might be useful. A projection of uniform circular motion undergoes simple harmonic oscillation.
• 16.7: Damped Harmonic Motion
Although we can often make friction and other non-conservative forces negligibly small, completely undamped motion is rare. In fact, we may even want to damp oscillations, such as with car shock absorbers. For a system that has a small amount of damping, the period and frequency are nearly the same as for simple harmonic motion, but the amplitude gradually decreases. This occurs because the non-conservative damping force removes energy from the system, usually in the form of thermal energy.
• 16.8: Forced Oscillations and Resonance
In this section, we shall briefly explore applying a periodic driving force acting on a simple harmonic oscillator. The driving force puts energy into the system at a certain frequency, not necessarily the same as the natural frequency of the system. The natural frequency is the frequency at which a system would oscillate if there were no driving and no damping force.
• 16.9: Waves
a wave is a disturbance that propagates, or moves from the place it was created. For water waves, the disturbance is in the surface of the water, perhaps created by a rock thrown into a pond or by a swimmer splashing the surface repeatedly. For sound waves, the disturbance is a change in air pressure, perhaps created by the oscillating cone inside a speaker. For earthquakes, there are several types of disturbances, including disturbance of Earth’s surface and pressure under the surface.
• 16.10: Superposition and Interference
Complex waves are more interesting, even beautiful, but they look formidable. Most waves appear complex because they result from several simple waves adding together. Luckily, the rules for adding waves are quite simple.
• 16.11: Energy in Waves- Intensity
• 16.E: Oscillatory Motion and Waves (Exercises)

Thumbnail: Mavericks Surf Contest 2010. (CC-SA-BY; Shalom Jacobovitz).

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