A study is made of the general behavior of a semi-active impact damper. The system consists of an undamped forced torsional oscillator, and a flywheel which can be locked to the oscillator through a clutch. The impact which results during clutch engagement is effective in reducing the vibration amplitude level of the oscillator when it is subjected to bounded excitation. All solutions of the system are shown to be bounded when the input is bounded. Periodic solutions are discussed in the following paper, Part II.

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