Stability
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Small Oscillations about an equilibrium position
Equations are omitted for technical reasons - download the original pdf
When an object in a stable equilibrium receives a small amount of energy it will oscilate about the stable position. If we assume that the system is conservative, then the object will (approximately or exactly) exhibit simple harmonic motion. A spring /mass system exhibits this kind of stability. [Diagram goes here - download the original to see it.] Its oscillations are given by; [Equation] where [Equation] is the stiffness of the spring ( recall that is the modulus of the spring if is its natural length. [Diagram goes here - download the original to see it.] A simple pendulum exhibits approximately simple harmonic motion- provided the angle of displacement, [Equation], is small. In such systems it is often easier to use the energy method to find the equation of motion- that is, to obtain the energy function and differentiate it.
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Contents of
Stability
1 Stability and Oscillations
2 Stability of the Equilibrium
3 Small Oscillations about an equilibrium position
4 Use of the second derivative of potential energy.
5 Oscillations involving rotation
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