# How does a driving frequency induce resonance if it is not exactly equal to the natural frequency?

To my understanding when the driving frequency is equal to the natural/resonant frequency of the object, there is constructive interference between the oscillations of the object and driving force. This causes the amplitude of the oscillations to increase. However if the driving frequency is not equal to the resonant frequency there is some periods of constructive interference and some periods of destructive interference, thus there is no net change effect on the amplitude of oscillations.

What I don't get is why doesn't the driving frequency have to be EXACTLY equal to the resonant frequency? If the driving frequency is exactly equal to the resonant frequency it will always be constructively interfering. However if the driving frequency is out by jut a small amount, to begin with it would interfere constructively as before (yes)?. But because the period is shorter (or longer) it would soon go out of phase, and then would it not be destructively interfering and, much like when the driving frequency is completely different to the resonant frequency, have no net effect on the amplitude?

Thanks in advance, if this question is poorly worded please ask for clarification and I'll try my best.

• Your confusion might arise from thinking of these oscillations as waves that can interfere. For example, if I am driving the oscillation of a spring on a mass, my force and the motion of the mass are not "interfering". The oscillation of the mass is determined by my force. It is not oscillating at some period and then my force comes along with a separate period that can be in or out of phase with the mass. – Aaron Stevens Jul 9 '18 at 17:26
• Energy is transferred in any event. But when the driving frequency matches the system resonance, the energy is transferred with maximum efficiency. – docscience Jul 9 '18 at 22:38