Humans can discriminate among the hardness of objects by tapping their surfaces. The damped natural vibration caused by tapping and its frequency are known to be the cue for the perception of hardness. This study is an investigation of the characteristics of this perception of hardness, as induced by vibration stimuli including multiple frequency components. We performed a comparative experiment using several damped vibration stimuli, which included either one or two frequency components, and investigated the significance of the secondary vibration mode and the change in its frequency. We found that the presence of the secondary mode significantly enhanced the perceived hardness; however, its frequency had a lesser effect on hardness perception.