Analyze Dampened Oscillations in Fluids: Math & Physics

In summary, the conversation discusses the topic of analyzing dampened oscillations in fluid mediums, specifically gravity waves near the surface of water. The necessary math and physics knowledge required for understanding this phenomenon is mentioned, including a calculus sequence, ordinary differential equations, and two semesters of introductory physics. It is also suggested to refer to books on the physics of waves and learn about partial differential equations and linear algebra. However, it is mentioned that a simple pictorial understanding can also be obtained through online research.
  • #1
Josh0768
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I am a layman with very little experience in math and physics and recently I became curious about how to analyze dampened oscillations occurring in fluid mediums, such as those following a disturbance in a pool of water. What sort of math and physics is required to understand this phenomenon and what sort of textbooks will cover things like this?
 
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Yes, there are gravity waves and capillary waves on the surface of water. Capillary waves are the very short wavelength waves that depend on surface tension, while the larger gravity waves are the longer wavelength waves.

How much math and physics you need depends on what your goals are. If you really want to understand the derivation and solutions of the equations, then you need at least the following:
a calculus sequence through multivariable and vector calculus, ordinary differential equations
2 semesters of intro physics

Then you will probably be ready to start looking at "physics of waves" kinds of books such as
http://farside.ph.utexas.edu/teaching/315/315.html

The actual equations of interest are partial differential equations, and while it might be nice to learn partial differential equations first, many students learn about them as needed in physics or engineering courses. It might help to also learn some linear algebra. For some of the relevant math (beyond the calculus sequence) one possible reference is
http://www.physics.miami.edu/~nearing/mathmethods/

If you just want a simple pictorial understanding, then I recommend googling to see what you find. Learning the derivation and solution of the partial differential equations won't necessarily yield any more understanding than you would get from a good qualitative description. It will, however, provide you will skills that are useful if you want to go further in science/engineering/mathematics.

jason
 
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Likes Josh0768 and vanhees71

1. What is the concept of dampened oscillations in fluids?

Dampened oscillations in fluids refer to the phenomenon where a fluid undergoes repeated back-and-forth motion, but with decreasing amplitude over time. This is due to the presence of external forces, such as friction or viscosity, that dissipate the energy of the oscillation, resulting in a gradual decrease in amplitude.

2. How is the motion of dampened oscillations mathematically described?

The motion of dampened oscillations in fluids can be described using differential equations, specifically the damped harmonic oscillator equation. This equation takes into account the damping coefficient, the mass of the fluid, and the frequency of the oscillation to model the behavior of the fluid over time.

3. What are the practical applications of analyzing dampened oscillations in fluids?

Understanding dampened oscillations in fluids has many practical applications, such as in the design of shock absorbers, tuning of musical instruments, and studying the behavior of ocean waves. It is also important in fields like meteorology and fluid dynamics, where the behavior of fluids is crucial in predicting weather patterns and understanding fluid flow.

4. How does the study of dampened oscillations in fluids relate to physics?

The study of dampened oscillations in fluids is a fundamental concept in physics, specifically in the branch of mechanics. It involves the study of forces, energy, and motion, and how these factors interact to produce the observed behavior of fluids. It also has applications in other areas of physics, such as electromagnetism and thermodynamics.

5. Are there any real-life examples of dampened oscillations in fluids?

Yes, there are many real-life examples of dampened oscillations in fluids. Some common examples include the motion of a pendulum in a viscous fluid, the vibration of a guitar string, and the movement of a boat on water. These examples demonstrate the impact of external forces on the oscillation of fluids and how they eventually lead to a decrease in amplitude over time.

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