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If a potential energy can be associated with a force, we call the force conservative. Examples of conservative forces are the spring force and the gravitational force. If a potential energy can not be associated with a force, we call that force non-conservative. An example is the friction force.
1.1 Simple harmonic motion 1.1.1 Hookeâs law and small oscillations Consider a Hookeâs-law force, F(x) = Â¡kx. Or equivalently, consider the potential energy, V(x) = (1=2)kx2. An ideal spring satisï¬es this force law, although any spring will deviate signiï¬cantly from this law if it is stretched enough. We study this F(x) = Â¡kx force because: