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.

A rescue operation is being conducted using a helicopter that lowers a stretcher on a strong but flexible cable. The helicopter hovers steadily as the stretcher, with a person on it, is gently lowered and comes to rest. After a while, the person on the stretcher starts to oscillate vertically (like a mass on a spring) due to slight air currents. The system behaves approximately like a mass-spring system performing simple harmonic motion (SHM). The effective spring constant of the cable is k=100 N/m and the total mass of the stretcher with the person is m=25 kg. The maximum vertical displacement from the mean position is 10 cm.

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.