The sound of your heart gives me an idea. The methodic thump thump thumping of a heart puts me in a trance that gives me great ideas. It’s a very inspirational sound, the sound of a heart is. It gives me an idea.
Alternatively, you could look at this kanji and see a "stand" radical and something that kind of (almost) looks like the kanji for "think." When you stand up and think, you come up with your very own ideas!
The heart of an eagle (い) is very strong. The person who knew this probably came up with the idea to make the bald eagle a symbol of the United States. Eagles are always flying around and doing things, so their hearts are very strong.