  In this paper we solve one dimensional trapped SU(2) bosons with repulsive
$\delta$-function interaction by means of Bethe-ansatz method. The features of
ground state and low-lying excited states are studied by numerical and analytic
methods. We show that the ground state is an isospin "ferromagnetic" state
which differs from spin-1/2 fermions system. There exist three quasi-particles
in the excitation spectra, and both holon-antiholon and holon-isospinon
excitations are gapless for large systems. The thermodynamics equilibrium of
the system at finite temperature is studied by thermodynamic Bethe ansatz. The
thermodynamic quantities, such as specific heat etc. are obtained for the case
of strong coupling limit.
