All structures are designed/built with certain forces such as load and other natural forces in mind.It would therefore be unreasonable to build stiff enough structures without giving them benefits of these forces.Consider a tree in the wind.What would happen if it did not sway in the wind? certainly,it would break up in many places just like glass.It is therefore imperative that the engineer does his calculations of the materials to be used to come up with a structure that can sway (resonate) reasonably or acceptably.There are standards of course. In this particular instance,the overpass resonates due to load or vibrations from adjacent roads or activities. It is therefore quite okay for the overpass to react that way

.Indeed,the worry should be,if it did not vibrate/shake/resonate at all.That one would surely not last. Also,as someone has put it,movements of such structures are also caused by expansion facilitation.
Nothing great was ever achieved without enthusiasm.