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Nintendo released the Rumble Pak for its Nintendo 64 alongside Star Fox 64 in April 1997, nearly a year after the console originally shipped in Japan and North America. The accessory was powered by two AAA batteries and designed as an add-on that attached to the gamepad's memory card slot, requiring you to swap the pack when prompted for saves.
Sony followed up with its DualShock controller later that same year, which was initially sold as a secondary peripheral for the original PlayStation and later included with an updated version of the console. The DualShock differed from the Nintendo 64's Rumble Pak in that it featured two built-in motors versus Nintendo's single external motor and it could power them directly from the PlayStation.
Four years later in 2001, Nintendo's GameCube shipped with a controller featuring an integrated rumble motor.