Difference between revisions of "Forest UCM Osc"

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In 1-D this force may be written as
 
In 1-D this force may be written as
  
:<math>F = - \frac{1}{2} kx</math>
+
:<math>F = - kx</math>
  
  
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2.) The work done is independent of path ( <math>\vec \nabla \times \vec F = 0</math> in 1-D and 3-D)
 
2.) The work done is independent of path ( <math>\vec \nabla \times \vec F = 0</math> in 1-D and 3-D)
 +
 +
==Potential==
 +
 +
:<math>U = - \int \vec F \cdot \vec r = - \int (-kx) dx = \frac{1}{2} k x^2</math>
  
 
=Simple Harmonic Motion (SHM)=
 
=Simple Harmonic Motion (SHM)=

Revision as of 23:00, 30 September 2014

Hooke's Law

The Force exerted by a spring is proportional to the spring displacement from equilibrium and is directed towards restoring the equilibrium condition. (a linear restoring force).


In 1-D this force may be written as

[math]F = - kx[/math]


Is this a conservative force?

1.) The force only depends on position.

2.) The work done is independent of path ( [math]\vec \nabla \times \vec F = 0[/math] in 1-D and 3-D)

Potential

[math]U = - \int \vec F \cdot \vec r = - \int (-kx) dx = \frac{1}{2} k x^2[/math]

Simple Harmonic Motion (SHM)

2-D Oscillators

Damped Oscillations

Resonance

Forest_Ugrad_ClassicalMechanics