"Could you clarify the terms resonance, vibration and damping"

Here are some succinct definitions...

  The increase in amplitude of oscillation of an electric or mechanical system exposed to a periodic force 
  whose frequency is equal or very close to the natural undamped frequency of the system.

  Random House Unabridged Dictionary



  The oscillating, reciprocating, or other periodic motion of a rigid or elastic body or medium forced from 
  a position or state of equilibrium

  American Heritage® Dictionary of the English Language




  The action of a substance or of an element in a mechanical or electrical device that reduces the degree
  of oscillation, vibration, or signal intensity.

  The American Heritage® Science Dictionary