Phase portrait of an oscillator
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Let us consider the phase portrait of a damped harmonic oscillator : a mass having two forces exerted on : the elastic force of a spring (spring constant ), and a viscous fluid force ( ) , where is the velocity of the mass .
The mass is displayed of with respect to its equilibrium position O.
The study is done in the inertial frame of reference of the laboratory.
Find kind of oscillations are these ?
Underdamping : since there is friction, the phase curve is not closed.
It ends in an equilibrium point (here, O) called an attractive point.
Graphically, find :
The initial position, .
The final position, .
The undamped period, .
The logarithmic decrement, .
Deduce the undamped angular frequency , the -factor of the oscillator, the spring constant and the viscous friction coefficient .
We deduce :
Note that gives the order of magnitude of the number of visible oscillations.