Q."Soldiers are not allowed to march on a bridge." Give reason.

Marching in step applies a periodic force to the bridge; if that frequency matches the bridge's natural frequency, resonance can build up dangerously large oscillations, so soldiers are ordered to break step.

Every structure, including a bridge, has its own natural frequency (or frequencies) of vibration, determined by its mass, stiffness, and geometry. When soldiers march in step, each footfall applies a small periodic force to the bridge at the frequency of their marching cadence.

If this marching frequency happens to be close to (or equal to) the bridge's natural frequency, the phenomenon of resonance occurs: even though each individual footstep applies only a small force, because the pushes arrive in phase with the bridge's own natural oscillation, their effects add up constructively over many cycles. The amplitude of the bridge's vibration can grow very large -- far beyond what any single footstep could cause -- potentially exceeding the structure's elastic limit and causing serious damage or even collapse (this is not just theoretical: it has caused real historical bridge failures).

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