Change of energy loss in driven oscillations

[ngc2024]

I find most textbook explanations of resonance lacking. My understanding is that resonance occurs because less "driving energy" is lost when the driven frequency approaches the natural frequency of a system. But why does the energy loss curve like this? Since Q-factor is different for each material or damping level, it must be caused by some intrinsic property of the system?

 

[gneill]

ngc20124, please remember that use of the homework formatting template is required for all questions posted in the homework areas of PF.

When a physical system is supplied with energy the system distributes, stores, and exchanges the energy via whatever mechanisms or pathways are available to it. For physical systems this means exchanging kinetic and potential energies along the way, whether mediated by electromagnetic or gravitational or other more "exotic" fields. Qualities like inertia enforce time dependence on the exchanges, hence we have acceleration versus instantaneous change in velocity (even if we often use the simplification of negligible collision times to analyze elastic collisions). So, for example, the speed of sound in a solid is not infinite: it progresses as a wave mediated by the electromagnetic force between the atoms of the material. Clearly the mass of the atoms and the strength of the inter-atomic forces play a role in the speed of the wave. And more importantly, energy can return along the same pathways if it is somehow stored and released or reflected at boundaries.

Resonance occurs when the supplied energy and the inherent energy distribution mechanisms are in sync, so that energy is supplied when the distribution mechanism is most ready to absorb and pass it along without the effects of existing energy in the system fighting it and trying to send energy back towards the source. The classic example is the adult pushing a child on a swing. The child and swing system has an inherent natural frequency that is determined by physical characteristics of the system. Energy supplied (as a push) enters the system and makes it move, and those movements are governed by the trading of kinetic and gravitational potential energy over time. The timing of the pushes that are most effective are clearly dependent on the natural period of the system.

While energy may be lost via damping mechanisms like friction, a big culprit is the fact that the energy supplied is fighting the existing motions (or energy states) of the system, and actually reducing motion or negating stored energy rather than adding to it.

The concept of inertia exists in all physical systems. In physical oscillators there's mass, while in electronics there's inductance and capacitance which tend to resist changes in current or potential. The tricky one is thermal systems where "heat" itself doesn't exhibit inertia, but most of the mechanisms that are involved in moving it around do and are tied to the masses involved (conduction, convection).

 

[ngc2024]

ngc20124, please remember that use of the homework formatting template is required for all questions posted in the homework areas of PF.

When a physical system is supplied with energy the system distributes, stores, and exchanges the energy...

Thank you, that was a brilliant answer!