Experiment 360 was the 360th genetic experiment created by Jumba with Hämsterviel's funding. He was designed to use his sleep-inducing bleat to cause his victims to instantly enter a near-permanent sleep. 360 and the other first 624 experiments were deactivated and smuggled to Earth by Jumba during his mission to capture Experiment 626.
All of the experiment pods were released and scattered across the island of Kauai.
360's pod was one of the twelve experiment pods recovered by Lilo and Stitch in "Drowsy". His was the final experiment pod that Pleakley, with some assistance from Stitch, cataloged after being convinced to do so by Jumba. Among the other pods were 102 (mislabeled 239), 204, 274 and presumably 604 (as his pod was seen with Jumba in "Houdini").
Since Lilo had become quite restless lately, Nani threatened to forbid her from doing any future experiment hunting if she was unable to fulfill her duties or be attentive, so Stitch attempted to get Lilo to fall asleep that night.
Eventually, Stitch activated 360 and used the latter's bleat to put Lilo to sleep. However, Stitch had no idea how to wake her up the next morning when Nani called for her. To try and solve the problem, Stitch tried to make Lilo seem awake by putting sunglasses on her, mimicking her voice, and moving her around like a puppet all over town.
Meanwhile, 360 escaped and was chased throughout Kauai by Jumba and Pleakley, while 360 put everyone he encountered to sleep by bleating. Pleakley initially caught 360 in his purse, but then opened it to put Gantu to sleep when the latter was looking for the experiment. At that point, however, 360 jumped out as Gantu fell heavily on Pleakley. Jumba then scolded Pleakley for letting 360 escape.
Stitch was unable to wake Lilo up all day, until Jumba revealed that the cure to 360's powers was to spray water in the victim's face. After Lilo was awakened, Stitch told her that she had to meet someone at the airport. Because she'd been asleep at the time, Lilo started to worry, but Jumba reassured her that Stitch had taken care of all her appointments.
Later, after a long chase, Gantu and Experiment 625 captured 360 in a duffel bag and guarded the Birds of Paradise Hotel. However, when they tried to use 360 to kidnap Regis Philbin (the man from the airport) while posing as bellboys, Lilo and Stitch were there for Regis since he disembarked, and protected him in every way they could.
Lilo eventually recaptured 360, named him Drowsy, and let Regis stay at the Pelekai residence for the night. In the end, Drowsy used his sleep-inducing powers to send Regis and everyone in Lilo's ʻohana to sleep.
In "PJ", Lilo used Drowsy to put Stitch to sleep after she claimed that Stitch had trouble sleeping lately, allowing Lilo to release PJ so she could avenge her strict substitute teacher. Strangely, however, Stitch woke up on his own.
In "Ploot", Drowsy was one of the second team of experiments (along with Finder and Babyfier) formed to try and stop Ploot. However, Ploot was easily able to defeat them, forcing the three experiments to retreat.
In "Remmy", Drowsy was one of the experiments in Lilo's dream.
The first 624 experiments, including Drowsy, were rounded up by Leroy and taken to a stadium to be destroyed. However, Lilo, Stitch, Jumba, Pleakley, Reuben and Gantu arrived before the experiments could be destroyed.
It is unknown whether or not Drowsy participated in the following battle between the experiments and the Leroy clones. However, it can be assumed that he participated by putting attacking Leroys to sleep.
The Leroys soon gained the upper hand in the battle, but were defeated when Lilo, Stitch, Reuben and several other experiments performed the song "Aloha ʻOe", which caused the Leroy army to shut down due to the original Leroy's fail-safe.
- Drowsy's sleep-inducing bleat and sheep-like appearance are likely derived from the mental exercise of counting sheep in an attempt to fall asleep.
- A recurring irony has occurred with Drowsy. Stitch originally used him to get Lilo to fall asleep, and in his second appearance, Lilo used him to put Stitch to sleep.
- Stitch somehow managed to wake up on his own while under Drowsy's effects, possibly indicating that other experiments are not affected as much.
- Drowsy's pod color is yellow.
- Drowsy is described by the experiment computer screen as, "Experiment 360. Primary function: Sleep inducer."
- Oddly, when Drowsy's image is reflected off of Stitch's eyes in The Origin of Stitch, he is not yawning for some reason. It is possible that Drowsy's yawning image was taken from Leroy & Stitch.
- Drowsy appeared on the DVD cover of Leroy & Stitch, along with Lilo, Stitch, Jumba, Pleakley, Doubledip, Fibber, Amnesio, Woody, Shredder, Ploot and Felix, with Leroy flying above in a one-man space shuttle.