Every spring/mass system executes vibrational movements as soon as it is excited. In real-world situations a distinction is made between two types of excitation:
- Shock excitation
- Continuous excitation
If a system is deflected out of its position of rest by a single impact - e.g. by punching - it oscillates at its vibration frequency (natural frequency) until the system's additional kinetic energy undergoes thermal conversion as a result of damping.
A continuously excited system - e.g. as a consequence of the residual imbalance of rotating machines - always oscillates at the excitation vibration frequency of the source of excitation (exciter frequency).
There is resonance if the vibration frequency of the source of excitation equals the system's natural vibration frequency. If the system had no damping, the amplitude of the vibrations would assume an infinite size.
The natural vibration frequency depends on the spring rate c and the value of the mass m. It is calculated on the basis of the following formula:
The natural frequency amounts to 1/60 of the value of the natural vibration frequency.
In the case of linear spring characteristics there is a direct relationship between the static spring deflection s - as a consequence of the mass m - and the spring rate c. Taking this into account, the natural vibration frequency or natural frequency can be determined as follows, provided the static spring deflection is known:
In the case of progressive or degressive spring characteristics, the value of the subtangent ssub must be inserted in the above formula instead of the real spring deflection s.