The vibration that takes place under the excitation of external forces is called forced vibration.
If excitation is harmonic, the system is forced to vibrate at excitation frequency . If the frequency of excitation coincide with one of the natural frequencies of the system, a condition of resonance is encountered and dangerously large oscillations may result, which results in failure of major structures, i.e., bridges, buildings, or airplane wings etc.
Thus calculation of natural frequencies is of major importance in the study of vibrations.
Because of friction & other resistances vibrating systems are subjected to damping to some degree due to dissipation of energy.
Damping has very little effect on natural frequency of the system, and hence the calculations for natural frequencies are generally made on the basis of no damping.
Damping is of great importance in limiting the amplitude of oscillation at resonance.