May 2022
Intermediate to advanced
487 pages
9h 22m
English
Content preview from Differential Equations, 3rd Edition
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5Applications of the Second-Order Theory
Vibrations and oscillations
Electrical current
Newton's law of gravitation
Kepler's laws
Higher-order equations
5.1 Vibrations and Oscillations
When a physical system in stable equilibrium is disturbed, then it is subject to forces that tend to restore the equilibrium. The result can lead to oscillations or vibrations. It is described by an ordinary differential equation of the form
In this section we shall learn how and why such an equation models the physical system we have described, and we shall see how its solution sheds light on the physics of the situation.
5.1.1 Undamped Simple Harmonic Motion
Our basic example will be a cart of mass ...
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