Forced Oscillations And Resonance

Resonance, discussed in NCERT Class 11, Chapter 14 (Oscillations), occurs in a forced oscillator when the frequency of the external driving force matches the natural frequency of the system, producing a very large amplitude response. If marching soldiers step in unison at a rate close to the bridge's natural frequency, the periodic driving force pumps energy into the structure each cycle, and the amplitude can grow until the bridge is damaged. Breaking step randomizes the driving so no single frequency dominates. The option about total internal reflection belongs to optics and reflection of waves, not bridge oscillation. The option of destructive interference of footfalls is wrong because the danger comes from constructive reinforcement, not cancellation. The option of Doppler shifting concerns changes in observed frequency due to relative motion, not amplitude build-up. A plausibility check: energy fed in at the natural frequency accumulates because the driving stays in phase with the motion, so resonance correctly explains the observed danger; the amplitude at resonance is limited only by damping.