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# Spring-mass system

## Video transcript

in the last exercise you probably notice that the simulation lack the natural bounciness of hair but what makes something look bouncy anyway to make this model bouncy we need each strand of hair to expand and contract slightly when forces are applied to them this required a new physical analogy to base or motto on so we tried Springs Springs are great because they can change length when you pull on them and to give the hair a little bit of weight we add a small weight to the end of the spring this is known as a mass spring system we can actually draw a mathematical model to explain what happens when a spring expands and contracts the model we use is based on a law developed by Robert Hooke a 17th century physicist Hooke notice that there are two things to consider when a spring expands and contracts one if we pull on a spring and it expands we will increase its length and it will pull back together two if the spring contracts its length will decrease and it will push apart how much a spring pushes and pulls is known as the spring force Robert Hooke was looking for a relationship between the spring force in the amount the spring contracts or expands we call this change in length displacement displacement is defined as the current length minus the rest length of the spring when we stretch a spring the displacement is positive in the resulting spring force is negative this is known as the pool force when we compress a spring the displacement is negative in the resulting spring force is positive this is called the push force so hoax observation was quite simple he noticed that a larger displacement results in a larger force while a smaller displacement results in a smaller force that is he noticed that the displacement is proportional to the force however every spring is different some take a lot of force to displace and some are really easy to displace so Robert Hooke introduced the idea of stiffness to account for how hard it is to displace a given spring it is represented with a letter K this led hook to his final equation which is known as Hookes law the spring force is proportional to a stiffness times the displacement notice that there is a negative sign there that's because we want a positive force when the displacement is negative and a negative force when it's positive if we plug this equation into the computer we get this realistic spring behavior for brave we model the horse's hair using a mass spring system similar to what we are describing in this tutorial nearly ten thousand simulated hairs in total in the next exercise you can explore a simple mass spring system you'll be able to adjust the following parameters mass of the particle spring stiffness K and the force of gravity and we'll ask you some challenge questions to make sure you understand the basics of Hookes law