What really is natural frequency and resonance?

Question

Shouldn’t the frequency of an object depend on how much I push it from one end if the other end is attached?

And what’s resonance? In my textbook there is no such explanation to what is actually is and the teachers are no help either. How is it so that if the forced vibration’s frequency are near the natural frequency, the amplitude will reach infinity? Logically the amplitude should increase with increase in force of the forced vibrations and not decrease.

Please help me understand this topic. Never have I been sooooo confused.

Answer 1

• Frequency is the number of cycles that are repeated per second. The number of back-and-forth repetitions of a child on a swing, you can say. This is just a general term used for anything that shows periodicity.

• Natural frequency, also called eigenfrequency, is the frequency that a specific object naturally will take if you just "let it go", influenced only by gravity. If you lift a child on a swing and let go, the frequency he will take in his swings is the natural frequency of this swing-and-child pendulum since no other forces than gravity are influencing. An object has a natural frequency as a describing property - even if you don't swing it. The natural frequency is the frequency that the object would take of swung.

• Resonance is what you achieve when an external periodic force is acting in synchronization and in phase with the natural frequency. You achieve resonance when you push the child on the swing just at the right time such that he goes higher and higher. But you could also push him out of phase, which would slow him down. So it's all about timing. Under ideal circumstances an external periodic force can indeed cause a periodic behavior to grow out of control of there is nothing to stop it. This is seen in bridge collapses where the wind pushes just happen to match the natural frequency of the bridge.