"The Locomotive Manipulation" is the first episode in which Sheldon initiates a kiss with Amy. Although initially done in a fit of sarcasm, he discovers that he enjoys the feeling. Consequently, Sheldon slowly starts to open up over the rest of the season, and starts a more intimate relationship with Amy. However, in the season finale, Sheldon leaves temporarily to cope with several changes and Amy becomes distraught. However, in "The Prom Equivalency", he hides in his room to avoid going to a mock prom reenactment with her. In the resulting stand-off, Amy is about to confess that she loves Sheldon, but he surprises her by saying that he loves her too. This prompts Amy to have a panic attack.
Raj meets with the woman his father set up for him, Anu. Her commanding personality and practical approach to marriage startle Raj but he agrees to go ahead with it. Howard criticizes him but apologizes; he just never expected Raj to give up on romance. Raj admits this to Anu so she proposes to him, and he says yes. Raj also sends out a relationship questionnaire to Leonard and Penny, which soon reveals that Penny does not think she ever wants kids, upsetting Leonard, who would like to have kids someday, and their friends selfishly badger them on the issue. After telling her father Wyatt who is also upset, Leonard tells Penny that he'll be okay with it, as he never thought he'd have her in his life. To get his mind off of it, Penny rents Leonard a Batmobile to drive in and have fun with for the day. Meanwhile, Stuart starts bringing home Denise at night, which is very uncomfortable for Howard and Bernadette. When they also try to have time to themselves, they wake up their kids.
Sheldon needs half a billion dollars to prove his latest concept of string theory, which the University cannot afford to fund. Crowdfunding and selling some of his most valuable comic books to Stuart give him a small start. When Raj mentions gambling in Las Vegas, Sheldon goes there but is caught calculating odds by security before he can make any bets. Meanwhile, Amy takes Penny and Bernadette shopping for her wedding dress. She loves an old-fashioned one that the other girls admit that they find ugly, though Penny assures Amy she can make her own decisions about her wedding. Sheldon, however, comes home and sees Amy in the dress and loves how she looks.