Final answer:
The term used for correcting unsynchronized marching steps among cadets is 'Correct Step.' It aims to bring back uniformity to the formation. Soldiers march out of step, known as 'route step,' across bridges to prevent structural damage due to resonance from synchronized steps.
Step-by-step explanation:
The term used to correct a cadet's steps to have synchronized movements when there is a mistake in marching is C. Correct Step. This command is given typically on the left foot and involves a small jump to get back in sync with the rest of the unit. The objective of issuing such a command is to re-establish uniformity in the marching formation without causing a significant disruption.
The reason why soldiers are sometimes ordered to "route step" or walk out of step across a bridge is related to the concept of forced oscillations. Marching in rhythm can set up resonance with the natural frequency of the bridge, which might compromise structural integrity and cause the bridge to sway or even collapse. To prevent this, soldiers break their synchronized steps to distribute the forces exerted on the bridge more randomly and reduce the risk of resonance.