Here’s an “ingelious” way to understand damping related to oscillations using this analogy.
Imagine a girl sitting on the swing oscillating with a natural frequency f0 with no damping.
A boy pushes the swing with a driving frequency fd.
For resonance occur where maximum energy is transferred from the boy to the swing, fd must match f0.
If fd is too high, the boy will be constantly pushing into thin air even
when the swing is away from him.
Converse, if fd is too low, the boy will be constantly pushing when the swing is already away from him.
Now if there is air resistance or damping, the apparent natural frequency f0’ of the girl will be < than f0 , since she is now oscillating slower.
In order for the boy’s frequency to match the swing, his driving frequency fd (matching f0’) must also be reduced to result in resonance. This is why with damping, the peak will occur at a lower fd.