Forced oscillations and resonance

Forced Oscillations: Resonance. Forced oscillations occur when an oscillating system is driven by a periodic force that is external to the oscillating system. In such a case, the oscillator is compelled to move at the frequency νD = ωD/2π of the driving force. ... The period TN of his oscillation is equal to 1/νN.

1. Forced Oscillations and Resonance

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3. Free Oscillation Definition of free oscillation : the oscillation of a body or system with its own natural frequency and under no external influence other than the impulse that initiated the motion called also free vibration opposed to forced oscillation

4. Forced Oscillations and Resonance Suppose now that instead of allowing our system to oscillate in isolation we apply a "driving force".  For example, in the case of the (vertical) mass on a spring the driving force might be applied by having an external force (F) move the support of the spring up and down.  Wd is the (angular) frequency of the driving force. the amplitude of these oscillations, B, depends on the parameters of the motion, W,Wd,m,b,F The amplitude, B, has a maximum value when W=Wd .  This is called the resonance condition. 

5. Natural frequency, driven oscillations, and resonance The oscillation frequency f of a system undergoing simple harmonic motion (e.g., spring+mass or pendulum) is said to be that system’s natural frequency .    If we apply an external, oscillating force that serves to “drive” the system at some driving frequency f d , then the system is able to absorb energy via the work done by the driving force.    The condition known as resonance is associated with the state that maximizes the efficiency of energy transfer from the driving force to the system.  Resonance occurs when the driving frequency matches the system’s natural frequency .

6. Theoretically