If I had to guess for most people one of the first times they saw hypnosis portrayed in the popular media was watching the Scooby-Doo, Where Are You! episode "Bedlam in the Big Top". Harry the Hypnotist (Barry Richards) tried to get revenge against a circus manager who sent him to prison years before for stealing from the circus company. Harry the Hypnotist disguised himself as a Ghost Clown and caused mischief to scare people away. In the end the criminal hypnotist was hoisted by his own petard. During his run though he caused trouble for some meddling kids and their dog.
Scooby-Doo (Don Messick) got hypnotized to walk the high wire rope. Shaggy (Casey Kasem) was hypnotized to be a lion tamer. Apparently nobody wanted to see Velma (Nicole Jaffe) get hypnotized. Ditto for Fred (Frank Welker). Last but not least one other member of Mystery Inc. fell victim to the hypnotic gold coin.
Image Source: Scooby-Doo, Where Are You!
For now let's skip speculating whether or not Harry the Hypnotist watched as Daphne changed into the circus ballet costume while under his control. I believe the animators had a lot of fun with the Daphne character under a hypnotic spell. I am surprised no fans seem to have made a live action reenactment of Daphne's brush with hypnosis. Maybe there was a video like that but it was taken down off YouTube and I just missed it. It's hard to tell due to DMCA.
Daphne riding a unicycle and nothing could stop her or get in her way. Entranced Daphne riding on top of elephants. Getting sprayed with water by an elephant. So much Freudian detail compressed into a few minutes of a Saturday morning cartoon.