I just want to add the vibration when permitted to continue will eventually lead to the strutural failure by fatique. People seldom investigate if a lamp post or flag pole breaks. They just replace it with another one. The vibration amplitude of a vertical cantilever from a street furniture can be alarmingly large. However each structure has a finite number of stress reversals, usually varies with intensity of the stress, which must be taken into consideration in the maintenace work.
@Craig H:
It's not that the first mode is being damped out by the mass of the lights; when you see a light mast swaying in the second mode, the system is being driven by a forcing function with a frequency which is close to the second natural frequency, rather than the first.
Vortices are shed from a cylinder alternately from the lift and right sides, with a frequency which is proportional to the wind speed, forming a "Karman vortex street", generating an oscillating lateral load on the cylinder. When the wind speed is such that the frequency of vortex shedding coincides with a structural frequency, resonance can occur, leading to an amplified response. (And also providing a positive feedback mechanism to lock-in the frequency of vortex shedding with the frequency of vibration.)
A typical light mast will therefore have one wind speed which tends to generate first-mode sway, and a higher wind-speed which tends to generate second-mode sway without generating a simultaneous first-mode response.
