A problem for IIT JEE aspirants

Consider the shown arrangement in which a thin rope ‘A’ with a linear density mA is connected to a thick rope ‘B’ with linear mass density mB. The thick rope passes over a pulley and is connected to a heavy block of mass M. The separation of fixed support S from a pulley is L. A stationary wave is setup in this composite string such that the joint remains a node. Given that mb = 4 kg/m, ma = 0.4 kg/m, M = 1 kg and L = 4l = 1 m. Under these conditions, find:

  1. The least possible frequency of vibration
  2. The total energy of vibration if the amplitude for both the string is A = 1 mm and the string vibrates at the frequency obtained in (a).