If a mechanical system is excited at a frequency close to its natural frequency, the vibration amplitude will be amplified causing noise or even failure. This natural frequency, for a system with a single degree of freedom without dampening can be calculated as:

$$f_n = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$$

where \(k\) is the rigidity of the system/part, and \(m\) is the mass.

So, in order to reduce the vibration level or resonance of the system/part, there are these options:

• Increase the stiffness to increase the natural frequency and move it away from the exciting frequency
• Add more mass to lower the natural frequency and move it away from the exciting frequency
• Increase dampening to lower the amplitude of the induced vibration, with the tradeoff that it widens the range of the response
• Decrease dampening to narrow the range of the response, with the tradeoff that it will increase the amplitude if the exciting frequency gets closer to the natural frequency
• Reduce the vibrations that are exciting the system/part