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  When an external force is applied to a spring, various vibrations occur depending on the conditions.
For example, if you add a weight to a suspended spring, the spring will begin to vibrate. In this way, the momentary external force applied when starting vibration is called free vibration.
　Then, after momentarily applying an external force, the spring performs constant vibration. Vibration that occurs at a constant frequency in this way is called natural vibration.
　However, the natural vibration of a spring is not constant forever because other external forces such as air resistance are applied during vibration. After some time the vibration will stop. This kind of gradual stoppage of vibration over time is called damping, and this vibration is called damped oscillation.

 Fig. 1 Free vibration

Momentarily moving a weighted spring causes the spring to start moving.

Fig.2 Natural vibration

A spring to which an external force is applied oscillates at a constant frequency as shown in Figure 2.

Fig. 3 Damped oscillation

After constant vibration, the amplitude of vibration decreases as time passes as shown in Fig.3.

Summary

1. Free vibration is when an external force acts momentarily and begins to vibrate.

2. Natural vibration is vibration at a constant frequency after applying an external force.

3. Damped vibration is when the amplitude gradually decreases.

 Spring vibrations are not limited to the above three.

When an external force, such as a damping force or a restoring force, which is not generated by the motion of the spring itself, acts periodically, a constant vibration can be maintained, and this is called forced vibration.

In addition, the natural vibration after applying an external force and the vibration period of the forced vibration after applying an external force may coincide, and this is called resonance.

Fig. 4 Resonance experiment diagram

Figure 4 shows an experiment in which a spring attached to a weight is moved up and down. It is an image of holding the tip of the spring with your hand, attaching a weight to the tip of the opposite side, and moving the spring up and down with your hand.
First, if you move the spring slowly from above as shown in ①, the weight will move slowly as well.
Next, if you move it a little faster like ②, the movement of the weight will also increase. This is resonance.
However, if you move the spring part as quickly as possible as in (3), the weight will hardly move.
The reason why this kind of phenomenon occurs is that the vibration that moves the spring from above and the vibration that moves from the weight overlap and suppress the vibration.

Generally speaking, in terms of the laws of physics, resonance always occurs when a spring moves.
For this reason, it is important to avoid resonance when designing springs.

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