Phase of Driven Vibration

The force driving an oscillation can be illustrated by holding a slinky in the vertical direction.

Move the hand up and down slowly:

• At low $f_h$, both the hand and the mass move in the same direction, and the spring hardly stretches at all.

Increasing $f_h$ makes it harder to move mass, and it lags behind the driving force.

At resonance $f_h = f_0$:

• the mass is 1/4 cycle behind the hand.
• the amplitude is at its maximum.

The higher the Q (quality factor), of the vibrating system, the more abrupt the transition in phase.