The amplitude oscillation due to wave-trapped particle interaction of absolutely unstable electrostatic ion cyclotron waves (EIC waves) in an ion beam-plasma system, its decay, and the generation of sideband waves as a normal EIC mode have been investigated. The external excitation of sideband EIC waves slows down the ion beam and deforms strongly the energy distribution of the ion beam. Then strong decay of absolutely unstable waves occurs. The generation of these two modes deforms the beam distribution, broadens its energy spectrum spread and randomizes the particle trapped in waves. The behaviors of waves and particles in agreement with numerical results based on a model of many wave-particle interactions.