Abstract: The vibration of a flexible rod with one fixed end and the other subjected to air resistance is studied.The boundary condition for the end with air resistance is established approximately.The eigen modes of vibration involve an exponentially decaying factor characterizing damp vibration,but are not of factorized form.Because the boundary conditions are not of Sturm-Liouville type,the theorem on the completeness and orthogonality of the eigenfunctions is not applicable. The vibration satisfying arbitrarily given initial conditions is found by the method of Laplace transform.

Key words: flexible rod, air resistance, vibration, Laplace transform