Natural frequencies of a multi-degree-of-freedom vibration system

A chain structured mass-spring vibration system with N degrees of freedom is considered where massesM _j = m_jm = m/j and spring stiffnesses k_j = c_jk = (N + 1 - j)k, j = 1, …, N, have been applied. The conjecture of Mikota [1] on the natural frequencies is discussed showing how difficult it is to find an explicit solution of the related eigenvalue problem. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)