in every book I own and on the internet, any information on forced oscillations is a version of the following definition, followed by the solution to a differential equation.
Forced oscillations: forced oscillations occur when a mechanical system is forced to vibrate by a periodic external force which continuously transfers energy into the system. The system vibrates at the forced frequency, whereas the amplitude depends on how close the frequency of forced vibration is to one of the natural frequencies.
I am looking for a more intuitive and physical explanation of what is actually going on, without blurring it with complex mathematics.
what is meant by the frequency of the forced vibration? I find "periodic" force a little vague. Does this mean that the force is such that it gives the oscillator impulses at regular intervals (like child on a swing) or can the force vary continuously?
secondly, why does the system (eventually) oscillate at the forced frequency?
Lastly, why does the amplitude depend on the frequency of forced vibration?
this one bothers me the most. Some books try to explain it that the closer you are the the natural frequency, the more "efficiently" the system absorbs the energy input, which sounds like hand waving to me. provided the damping is kept constant, where does the rest of the energy go and why is it absorbed the greatest at the resonant frequency?( I am aware of real life examples and am looking for a more general explanation)