The well-behaved solution of the hydromagnetic wave equation for a general class of initial conditions is used to study the ringing, phase-mixing, transient amplification of field line resonances. An expression for the phase-mixing time in terms of the amplitude of initial impulse at the magnetopause and the gradient of Alfven speed in the magnetosphere is derived. The features of free oscillation of field lines studied here compare well with the previous numerical studies for particular types of impulse excitations of the magnetosphere. ¿ American Geophysical Union 1995