Abstract: In this paper, the analytical solutions of Bloch equations under various physical conditions are given by means of Laplace transformation.Those solutions have clear physical pictures and are easy to be used.They have ban put in the use of the solvent peak suppression and Shaped pulse design.About solvent peak suppression,the approximate formulae of suppression efficiency's limit and optimum suppression time are given.In design of Shaped pulse,we think that all four kinds of solutions in Bloch equations have to be taken into account.It is also shown by simulation that if the same frequency function excited by pulses for different flip angles are required,the shape of pulses in time domain must be modified. A series of experimental results coincide well with the above conclusions.

Key words: Analytical solutions of the Bloch equations, Solvent peak suppression, Shaped pulse