Consider a homogeneous linear chain with one inclusion, i.e. we assume that the elastic support number n = 0 possesses a stiffness which differs from other ones: γ n = γ + ΔγS 0n (S 0n is the Cronecker symbol). The following equations govern oscillations of the considered chain (12.1) % MathType!MTEF!2!1!+- % feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbiaeaaca % WG1baaleqabaGaaiOlaiaac6caaaGcdaWgaaWcbaGaamOBaaqabaGc % cqGHsislcaWGJbWaaeWaaeaacaWG1bWaaSbaaSqaaiaad6gacqGHsi % slcaaIXaaabeaakiabgkHiTiaaikdacaWG1bWaaSbaaSqaaiaad6ga % aeqaaOGaey4kaSIaamyDamaaBaaaleaacaWGUbGaey4kaSIaaGymaa % qabaaakiaawIcacaGLPaaacqGHRaWkdaqadaqaaiabeo7aNjabgUca % Riabfs5aejabeo7aNjabes7aKnaaBaaaleaacaaIWaGaamOBaaqaba % aakiaawIcacaGLPaaacaWG1bWaaSbaaSqaaiaad6gaaeqaaOGaeyyp % a0JaaGimaaaa!58CF! $${\mathop u\limits^{..} _n} - c\left( {{u_{n - 1}} - 2{u_n} + {u_{n + 1}}} \right) + \left( {\gamma + \Delta \gamma {\delta _{0n}}} \right){u_n} = 0$$ .