Even a very close reading of Rodman Philbrick's novel Freak the Mighty does not reveal a specific time period in which the novel takes place. The reader must infer when it takes place based on the clues that are given. Some authors use historical events as the setting of their novel, and others use cultural references to help readers understand the time frame in a novel. Rodman Philbrick does not use historical events, and the cultural references he uses are vague. He created a story that readers can relate to across many generations. In my opinion, it is a modern classic.
There are several clues given that place the novel in modern times, but even those clues could still span a time period from about the 1980s through the 1990s. For instance, Max attended daycare, a very common thing to do in modern times. He attends school and rides a bus. He and Kevin attended a fireworks display put on in a city park on July 4th. In chapter 4, Kevin drags a rusty, red American Flyer brand wagon from under the steps of his house. This is a very good clue to the time period of the novel. I had this type of wagon, and I grew up in the 1980s. If you left it out in the rain, it would rust, so the fact that this wagon is rusty does not belie its age. I would say this clue is evidence that the novel is set somewhere between the late seventies and the early 1990s.
Another clue to the time period is Kevin's interest in robots. Kevin is fascinated by robots, and, according to him, robots are a huge industry in the time when this novel is taking place. Here is one thing Kevin has to say about robots:
Robots are not just in the movies. Robotics, the science of designing and building functional robots, is a huge industry. There are thousands of robot units presently in use. Millions of them. They don't look like the robots you see in movies, of course, because they're designed for function. Many robotic devices are in fact sophisticated assembly units, machines that put together cars and trucks and computers. For instance, the space shuttle has a robot arm.
The first space shuttle was launched in 1981. The way Kevin talks about it, it seems like a part of everyday life, so it is likely that the book takes place after 1981. Later in the same chapter, Kevin and Max talk about watching Star Trek on TV. This show aired from 1966-1969, but it is still in syndication (re-runs) today. Star Trek: The Next Generation did not start until 1987. It is possible Kevin and Max were referring to this show, placing the novel in the late 1980s or the early 1990s.