Question

Sameena made a setup in the following manner. A spring having a spring constant 1200 N m-1 is mounted on a horizontal table as shown in Fig. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released.

Assertion: Resonance is special case of forced vibration in which the natural frequency of vibration of the body is the same as the impressed frequency of external periodic force and the amplitude of forced vibration is maximum. Reason: The amplitude of forced vibrations of a body increases with an increase in the frequency of the externally impressed periodic force.

A group of soldiers is marching in step across a long suspension bridge. The rhythmic marching causes the bridge to begin oscillating slightly. The bridge is modelled as a large mass-spring system, with a natural frequency of 2 Hz. Each soldier exerts a force at a frequency of 2 Hz, in sync with the natural frequency of the bridge. This creates resonance. The oscillations gradually increase in amplitude until the soldiers are ordered to break step and walk randomly to stop the resonance.