Abstract: This paper discusses identifiability of the initial state of one vibrating
string with viscous damping at end point，where the velocity at this po-
int is observed.An abstract semigroup approach is used here .It has been
proved that the system is a spectral system，and the identifiability depends
completely on the measurement of the observation time interval
In addition，the classical solution to the initial-boundary value problem is
obtained under certain assumption of the initial value.