2008-Witthansen-ExamplesOfDifferentialEquationsInPhysics

By Brian Winkel

SIMIODE, Cornwall NY USA

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Abstract

Witt-Hansen, Ole.  Examples Of Differential Equations In Physics.  Article. 29 pp. Source: www.olewitthansen.dk . Accessed 27 November 2017.

This is an article from the author’s homepage. The work contains fundamental and basic background and derivation of the differential equation models for a number of phenomena. We list the index here.

1. The dependence of pressure with altitude.............................................................................. 4

2. Radioaktive chains of decay .................................................................................................. 6

3. Linear motion of a particle in liquids and gasses................................................................... 9

3.1 A ball sinking in a liquid...................................................................................................... 9

3.2 Vertical motion with turbulent resistance in liquids and gasses ........................................ 11

3.2.1 Upward movement .......................................................................................................... 12

3.2.2 Downward movement: .................................................................................................... 14

3.2.3 Vertical motion in air ...................................................................................................... 14

4. The motion of a projectile .................................................................................................... 16

4.1 The motion of a projectile without drag............................................................................. 16

4.2 The motion of a projectile with drag (air resistance) ......................................................... 17

5. Damped harmonic oscillations............................................................................................. 19

5.1 Solution to the differential equation using complex numbers. .......................................... 20

5.2 Traditional solution of the same differential equation ....................................................... 22

6. Forced harmonic oscillations without damping ................................................................... 24

7. Numerical solution to differential equations........................................................................ 27

7.1 Taylor’s formula ................................................................................................................ 27

7.2 Numerical solution to first order differential equations..................................................... 28

Keywords: differential equation, mode, decay, oscillation, projectile, sinking, motion, damped, numerical, Taylor’s formula

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Researchers should cite this work as follows:

  • Brian Winkel (2017), "2008-Witthansen-ExamplesOfDifferentialEquationsInPhysics," https://simiode.org/resources/4351.

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