Damping

(jumping, bouncing) (light switches on) - Now that we have a spring simulator, let's address a problem we faced in the first lesson. Previously, we tried only using springs to model our strands of hair. That resulted in a hair which was really bouncy. Fun, yes, but not very realistic. To address this we added a damper to each spring. Remember, dampers resist changes in velocity causing our springs to settle down much more quickly. Mathematically, a damper is quite simple. We can think of the damper as a new force which acts in the opposite direction of the spring force. The size of this source will depend on two things. First, how strong the damper is, we'll call that the damping coefficient. Second, the velocity of the spring displacement. If the spring is stretching or compressing very quickly, the damping force will be large and if the spring isn't moving, there's no damping force since there's no movement to resist. We can use a really simple equation to describe this situation. Damping force equals damping coefficient times velocity of the product. Okay, let's add this new force to our system. At the top of our program we need to initialize a new variable called damping. Earlier, we called this the damping coefficient. Zero means no damping and the higher the number the stronger the damper is. Now we can move into our draw function and define this new damping force. Right below our spring force calculation I'm going to define a new variable called damping force Y and it will be equal to damping times velocity Y. Next we add this force to our existing force Y calculation. Currently, we are only taking gravity and spring force into consideration. Now we need to subtract our damping force Y since it resists the spring force. Okay, let's try this out. Here's the response with no damping. We call this system under-damped since it bounces forever. Let's try increasing our damping variable to one. Notice it comes to rest more quickly. This is getting better, but if I set damping to something huge, like 100, we run into a problem. This is called over-damping. The spring barely moves. This isn't realistic. The trick is to find the right balance of spring stiffness and damping to get realistic motion. Let's pause here so you can try this out for yourself. Try experimenting with the damping and spring force coefficients to get a realistic behavior. Good luck.