To discuss several problems in the process of establishing and solving equations of motion in structural dynamics teaching. It mainly includes the difference of stiffness coefficients between dynamic and static mechanics as well as their relationship by the static condensation, the Fourier transformation condition from impulse response function to frequency response function and their effect on dynamic response, the frequency response function of the hysteretic damping system. The theory analysis and numerical results show that: (1) For the lumped-mass system with only translational degree of freedom, the stiffness in dynamics is the force required along DOF due to unit displacement at translational DOF and relaxation of rotational DOFs, and the stiffness coefficients obtained by the static condensation method and the unit displacement method are identical; (2) Whether a system with damping or not, the Fourier transformation relationship between the frequency response function and the impulse response function is accurate; the particular solution includes steady-state vibration and free adjoint vibration in the time domain, however, only the steady-state vibration in the frequency domain. Their difference is evident for the initial stage of vibration. The difference is more noticeable for small natural frequency. (3) For a system with hysteretic damping, the frequency response function of the negative frequency should be the conjugate function of that of the corresponding positive frequency.