A number of structures in industrial facilities are installed on supports, and there have been cases in which damage to such structures has been caused by coupled vibration. In seismic design procedure, the response magnification is obtained from the natural frequency and the modal damping ratio of the coupled system between the structure and the supportive structure. Therefore, the simplified estimation method for calculating the natural frequency and the modal damping ratio of the coupled system is required in the seismic design. In the past study, an equation to calculate the modal damping ratio of a coupled system was presented. The proposed equation was useful for obtaining the modal damping ratio without performing an eigenvalue analysis or a shaking test. In current seismic design procedure, for simplicity, the design response spectrum is used to estimate the acceleration response magnification of a system having one degree of freedom (1-DOF). Though the response magnification of a coupled system can be calculated based on the response magnifications of the 1st mode and the 2nd mode, the participation factor and modal matrix of the coupled system are required. In order to obtain the response magnification, a simpler method that does not involve the participation factor or the modal matrix is proposed, and the characteristics of the proposed method are examined.