Tolerance of Natural Frequency & Resonance?

I'm writing a report at the moment about natural frequency, driving frequency and resonance - and I was wondering, is there a typical % tolerance inside which the driving frequency will cause resonance (or exhibit resonance-like characteristics)? Or does this tolerance depend with the material and construct involved?

Note- I'm writing about an oscillatory system - torsion pendulum, so it would be resonance in an oscillatory sense).

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The answer will depend on whether you are considering only simple linear undamped oscillators or more complex cases with damping or non-linear behavior. It might be too much to try to describe every possible outcome so perhaps you should specify a bit more. –  Philip Gibbs - inactive Jan 6 '12 at 23:45
The system has very (constant) light damping (in order to limit the maximum amplitude of oscillation) but I am considering only the linear behaviour - just interested to see how far from natural frequency an oscillator will begin to exhibit resonance-like characteristics. –  George Pearce Jan 6 '12 at 23:58

An oscillator is usually characterized by its quality factor Q. This is a dimensionless parameter which measures how "good" of an oscillator it is. It also relates to the quantity you are interested in - a linear, damped oscillator will exhibit a lorentzian peaked response in the frequency domain. The bandwidth of the resonance (points where the response is decreased to 50%) is given by $\Delta f = \frac{f_0}{Q}$.