Abstract: The method of separation of variables for the vibration of an flexible rod with end surfaces subject to air resistance is discussed again.Generalized orthogonal relations of the complex eigenfanctions are established.The general solution is expanded in terms of complex eigenvibrations.The orthogonal relations are used to determine the coefficients in the general solution,such that it satisfies arbitrarily given initial conditions.Several cases with many boundary conditions are solved,including the case with both ends subjected to air resistance,and the case with one end fixed and the other connected to a concentrated mass and the latter connected to a spring and subject to air resistance.

Key words: flexible rod, air resistance, vibration, method of separation of variables