A child of mass is sitting on a swing made of a light seat suspended by two long…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A child of mass 25kg is sitting on a swing made of a light seat suspended by two long ropes each of length 2.50m. Assume that the swing executes small–amplitude oscillations so that it may be treated as a simple pendulum.
(a) Calculate the natural time period and natural angular frequency of the swing.
(b) The child’s parent gives successive pushes with equal magnitudes at two different intervals: first every 2.8s and later every 3.2s. In which case will the amplitude of swing grow faster? Justify your answer.
(c) The ropes are now fitted with broad fabric streamers that increase air resistance. Explain qualitatively how this additional damping will modify (i) the maximum amplitude achievable when pushing exactly at the natural period and (ii) the range of driving periods over which a noticeable increase in amplitude is obtained.