# How Can You Model a Realistic Bouncing Ball Using Springs

Take a ball and drop it on the ground. Yes, it will bounce back up. However, it doesn’t return quite to its starting height — it never does. Even a “super bounce” ball doesn’t return to its starting height. Why? Well, one way to think of this is that the ball starts with some gravitational potential energy that is converted to kinetic energy as it falls. When it collides with the ground, some energy is then transferred into thermal energy in the ball and ground. This means it has less total energy to get up to the starting height.

You can measure the difference in starting height and bouncing height to calculate the coefficient of restitution (how bouncy it is). Here is my data on that bouncing stuff.

But how can you build a model of a bouncing ball that makes it act like a real ball? Oh sure, you could just put some fudge factor in there that reduces the kinetic energy after each bounce — but what about a more fundamental method?

**Perfect Bouncing Ball**

I’m going to get to this real bouncing ball, but let’s start with a model of a perfect ball. This one will fall down, hit the ground, and then bounce back to the same height that it started with. I’m going to make this work with a spring. Yes, the ground will be a spring such that during impact it will push against the…