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frequency of pendulum
Every pendulum connecting with a piece of string should have its own natural frquency. If driving force is applied to the pendulum, the frequency no longer follows its natural frequency.
1. Is it correct to say we can change the frequency of the pendulum to any value we want if a changeble driving force is applied?
2. If we increase the driving frequency, that means we increase the power applied to the pendulum system. Then, why the amplitude of the pendulum doesn't increase? Is it correct to say the damping force also increases? If yes, what is the reason of the increasing damping force except because of air resistance? Is it related to the phase difference or other reasons? How does the provided energy dissipate?
- ?Lv 71 十年前最愛解答
Without goinf into details of the complex mathematical formulation for a forced oscillation, it is interesting to look at an animation of a forced oscillation system using the following link. You could obtain answers to your questions by observing the animation through changing of the driving frequency.
1. Select "elongation diagram" on the righ hand panel. This display the displacement-time curves for both the driving force and the oscillating mass. By changing the frequency of the driving force, you can see that the frequency of oscillation of the mass is also changed and is the same as that of the driving force, though in some cases, there is a phase difference.
2. Select'amplitude diagram" or just remain at "elongation diagram". You could see that the amplitude of vibration of the oscillating mass, in fact, increases with the driving frequency before reaching resonance. But the amplitude decreases with increasing driving frequency after passing the resonance frequency.
The reason for such behaviour of amplitude change is mainly because of the phase difference bewteen the driving force and oscillating mass. At resonance, the energy delivered to the oscillating mass from the driving force is maximum. At other frequecies, the energy transfer becomes less.