A vibration absorber is a mechanical device which is tuned to reduce or eliminate undesired vibrations, it must shift the natural frequencies, away from the excitation frequency, as shown in Fig. 1.

Fig. 1 Comparing response of system, with and without absorber

An additional spring mass system is attached to the main spring mass system, so that the resonance of the original system will not occur. The addition of spring mass system results in a two degree of freedom system, having two natural frequencies. General applications include reciprocating tools such as saws, drills, rotary hammers which requires to balance the reciprocating force. Fig. 1 shows a schematic representation of an undamped dynamic vibration absorber.

Fig. 2 Undamped dynamic vibration absorber.

Mathematically, a mass m₂ attached to a machine of mass m₁, through a stiffness of k2, will be

By assuming harmonic solution,

The steady state amplitudes are,

To reduce amplitude of m₁, X₁ is substituted as zero, leading to

The absorber is designed such that the amplitude of vibration of the machine, while operating at its original resonant frequency, will be zero.
By defining,

and the natural frequency of m₁ and m₂ as ω₁ and ω₂ ,

The steady state amplitudes can be written as,

At ω=ω₁ substituting X₁ = 0, which gives,

This shows that the force exerted by the auxiliary spring is opposite to the impressed force, neutralizing it, thus reducing X₁ to zero.