The dynamic properties of the particle motion, formation of colloidal crystals and phase transitions in plasma-dust systems are important fundamental questions [1].The cases mostly studied, experimentally and theoretically, correspond to oscillations and lattice modes in the chains of electrically charged dust grains [2,3] . The magnetic moment of a spherical particle can be written as m i =4 πa 3 M i /3 where M i is the particle's magnetization. The Euler-Lagrange equations (we also add the phenomenological friction 2γṘ) for motion and rotation in all three dimensions are cumbersome and for simplicity we assume that motions are linear and only in the (x, z)-plane,, and R i =( x i ,0 ,z i ). In the studied case, there are two possible equilibria: (1) when all magnetic moments are aligned in the z-direction, i.e. parallel to the external magnetic field, and (2) when all magnetic moments are aligned along the chain and perpendicular to the external magnetic field.For small oscillations of the centers of masses in the x-direction of vertically