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great work making it this far now it's your turn to drive so far we've built a two-dimensional mass spring system it's pretty cool it's the key building block from many simulations recall in Lesson one we use multiple Springs connected together like this to model hair in this video I'm going to show you how to add a second spring and mass to your system first let's draw a new force diagram to see what's going on let's call our two masses mass one and math two and our two Springs spring one in spring two first let's think about the new forces acting on mass one as before we have the gravity force acting downward a spring one force pulling up towards the anchor and a damping force acting in the opposite direction however now there is a new force due to the new spring connecting math to in this case the displacement we use to calculate spring to force is the difference between both masses mass to position minus mass one position and there is also a damping force resisting the spring to force so we need to add these two new forces to the X&Y components of the mass one net force calculation now consider the new mass we've added it will experience the force of gravity as well as a spring to fourth minus the opposing a spring to damping force that's it for modifying our for speculation at the top we'll need new initial variables to represent both the position and velocity of mass two I'll set the initial position of mass two so that it's below mass 1 the initial velocity of mass 2 is 0 as well to add a new mass - we have to double up all of our equations used for mass 1 however there are two key differences for the mass to spring forth calculations will use mass to position minus mass 1 position as our displacement and for the mass to net force calculations we have mass 2 spring force minus mass 2 damping force finally we just need to draw the new circle in line for this massive spring the new line works sent from as 1/2 mass to the new circle will be the center of mass two's position and that gives us this mass spring systems are really powerful at Pixar we don't just use them for hair the trees of the good dinosaur were also simulated with the mass spring system kind of similar the hair but it had to represent a tree structure trees have branches so we simulated them by having multiple line segments attached to each other kind of like having hairs attached the hairs instead of only being attached to the scalp even clothing is simulated using masses and springs in braves Merida had several garments that we needed to simulate and each garment had their own spring values these values were chosen to mimic different kinds of cloth such as wool cotton and satins as you can see mass spring systems are super useful for modeling and simulating all kinds of different things see if you can think of other materials that could be created using mass spring systems and that's the goal of this final project your job is to modify this program to make whatever you can dream up the program you spin-off will automatically show up below under the spin-offs tab along with everyone else's and I really encourage you to check out other creations to get new ideas for inspiration have fun and happy exploring