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Oscillations

Equation of motion


Following Newton's laws, we have

F = ma


where a represents the acelleration of the object.
The acelleration is given by the second time derivative of the displacement. We obtain

m d2u/dt2 = ma = F = - Celu


We thus end up with the second order differential equation given by

d2u/dt2 = - (Cel/m) u


Solutions describe the motion of the oscillating object.


Harmonic motion