Analyze Dampened Oscillations in Fluids: Math & Physics

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SUMMARY

This discussion focuses on analyzing dampened oscillations in fluid mediums, particularly gravity and capillary waves. To thoroughly understand this phenomenon, one must study calculus through multivariable and vector calculus, ordinary differential equations, and complete two semesters of introductory physics. Recommended resources include the "Physics of Waves" course from the University of Texas and a math methods reference from the University of Miami. A qualitative understanding can be achieved through simpler resources, but mastering the underlying mathematics is essential for deeper scientific exploration.

PREREQUISITES
  • Calculus through multivariable and vector calculus
  • Ordinary differential equations
  • Two semesters of introductory physics
  • Basic linear algebra
NEXT STEPS
  • Study the "Physics of Waves" course at the University of Texas
  • Explore partial differential equations in physics or engineering contexts
  • Review the math methods reference from the University of Miami
  • Research qualitative descriptions of gravity and capillary waves
USEFUL FOR

This discussion is beneficial for students and enthusiasts in physics, mathematics, and engineering who seek to understand the dynamics of fluid oscillations and wave phenomena.

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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