There are so many ways to describe that someone has a "motivation" in Mandarin. However, "动机“ is no that often used in daily cases, such as going to the gym, because "动机“ is extremely formal and academic and even a little bit derogatory, which implicates that someone has a complex mental state and intends to something negative for his or hers own benefits. In a common sense, I think we Chinese usually use "让“ in daily cases to show motivation and sense of "cause and effect". For example, you can say "他的建议（his advice）让（motivated）我（me）重新去了体操馆（to start going to the gym again）“. Also, there are other more complex and delicate ways to show "motivation" such as "促使“（stir, makes, results with some outer factors)，”打动“（motivates mentally）,”点燃了……希望的种子“（fire the seeds of hope to do something again).

Hi, Jake I am happy to answer your question here, and "motivate"is "促进" in Chinese.Hope my answer can help. Helen

刺激／激励 may work in this case.