Abstract

Citation

Researchers should cite this work as follows:

• Witt-Hansen, O. (2023). 2017-Ole_Witt-Hansen-Examples Of Differential Equations In Physics. SIMIODE, QUBES Educational Resources. doi:10.25334/HXHX-ZG52

  BibTex | EndNote

Article Context

Description

Witt-Hansen, Ole.  2017. Examples Of Differential Equations In Physics.  Article. 29 pp.

Source: www.olewitthansen.dk . Accessed 27 March 2023.

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