Understanding Resonance: Causes and Effects in Oscillating Systems

[Harmony]

Why does an oscillating system under resonance oscillate with the largest amplitude? And why does resonance occur when the driving frequency match the natural frequency? Can resonance occur at frequency other than natural frequency?

 

[twobagger]

Why does an oscillating system under resonance oscillate with the largest amplitude?

Because, in absence of a damping force, the driving force and the velocity of the system have the exact same direction. Therefore, a positive amount of work is constantly being done, and therefore, the mechanical energy of the system is increasing.
So, the amplitude will, in absence of a damping force, increase without limit.

And why does resonance occur when the driving frequency match the natural frequency?

Because, since the driving frequency matches the natural frequency, the direction of the driving force matches the direction of the oscillating system's frequency.

Can resonance occur at frequency other than natural frequency?

I'm pretty sure it can't.