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When the thickness of a structure is reduced to decrease weight, it may experience structural vibration and disturbance. The use of passive patches is effective in addressing this issue when the loss factor is small or when space and weight are restricted. The greatest attenuation occurs when passive patches are used across the entire coverage area. However, passive patches of reasonable size must be affixed to ensure that they are effective in terms of cost and design. In this paper, the sum of squares' value for the bending mode shape is used to determine the location of a small passive patch to achieve vibration damping for multiple modes. Under the condition of forced vibration, the modal contribution of each mode is obtained. Using this contribution as a weight, the optimal position of the passive patch is determined as the maximum value obtained in the form of a linear combination multiplied by the curvature of the beam. Simulation and experiment were used to test the efficacy of the location determined for passive patches. It was determined that, depending on the location of the passive patch, the peak amplitude at the natural frequency of each mode decreased significantly, validating the effectiveness of the design method. [ABSTRACT FROM AUTHOR]