Free to Forced Harmonic Oscillator Transition In this animation, I will show the transition between a freely oscillating damped harmonic oscillator to a Fd oscillator where the phase of the F is different from the initial phase of the free oscillator. Both the initial phase difference and the difference between the frequencies of forcing motion and the free oscillator will be variables. How this transition occurs is a question that should arise in any driven resonance experiment. It should be obvious that, when a sinusoidal F (usually in the form of an incident electromagnetic (EM) field) FIRST impinges on an oscillating object, it is just as likely to slow the oscillation as it is to speed it up depending on the relative phases. One might then conclude that the F, on average, does nothing to increase or decrease the energy of the oscillator which is tantamount to saying the its temperature does not increase or decrease. But ultimately the F WILL prevail and will drive the damped oscillator at its own frequency and with a phase difference that depends on the drag coefficient and frequency difference between the Force frequency and the free oscillator frequency. This animation will show that, sometimes during the transition to a steady state Forced oscillator, the energy of the oscillator will actually be transferred to the entity that is driving the F. In the animation plots, the black trace (usually covered by the blue trace) is the numerical integration of the acceleration induced by the spring and the Force. The blue trace is the algebraic displacement given by teh equations in the link below. The green trace is the energy associated with the speed of the mass and the displacement of the spring. The spring length conforms to the distance between its fixed anchor at the bottom and the displacement of the mass. After a time 5/alpha the motion and the plots restart. These also restart when any of the 7 slider values are changed.
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wF k yDot0 F y0 b mass Single Step