Every object can oscillate about its equilibrium position when displaced by an external force. When a particular body is displaced from its equilibrium position, the body starts oscillating with its own natural frequency \(\omega _\text{n}\).
If you apply an external periodically varying driving force on the oscillator, you can change the frequency of the oscillating body in your need called driving frequency \(\omega_d\). And the corresponding periodically varying force is called driving force.
When the natural frequency of the oscillator is equal to the driving frequency of the external force, the amplitude of the resultant oscillation increases dramatically.
The effect of the largest amplitude peak obtained when \(\omega_d\) equals \(\omega_n\) is a phenomenon called resonance.
In Figure 1 you can see how the amplitude of a forced oscillation increases when the frequency of an external force nears the natural frequency of the oscillator.
In Figure 1 you can also see different curves for the same oscillator for different damping forces - greater the damping force, lower the amplitude at resonance. In curve \(a\) the damping force is lesser than the damping force in curve \(b\). And in curve \(b\) the damping force is lesser than the damping force in curve \(c\).
That's the reason why solders are said to stop marching while crossing a bridge to avoid destructive effect. The reason is that when the solders march over a bridge, the driving frequency of their marching may nearly equal to the natural frequency of the bridge and the bridge can oscillate with the greatest amplitude possible due to the phenomenon of resonane which can destroy the bridge.
