A child of mass 30kg is seated on a rigid swing suspended by two light ropes, each of length 2.5m.
(i) Treating the swing as a simple pendulum, derive an expression for its natural period T0 in terms of the length L and acceleration due to gravity g.
(ii) Calculate the natural period and the corresponding natural frequency of the swing for g=9.8m s−2.
(iii) The child’s father gives a small push each time the swing passes through its lowest position. For the amplitude to build up steadily, what should be the time interval between successive pushes? Give reason for your answer.
(iv) Gentle air resistance acts on the swing, providing a damping force proportional to its speed. Explain qualitatively how such damping affects (a) the rate at which the amplitude builds up under periodic pushes and (b) the sharpness of the resonance condition.