SIMPLIFIED: "15.2: Hooke's Law"

Link: https://phys.libretexts.org/Bookshelves/University_Physics/Physics_(Boundless)/15%3A_Waves_and_Vibrations/15.2%3A_Hookes_Law 

Note: The above image is from the original article.

The article linked above talks about Hooke’s Law! It also has some information about elastic potential energy which I will also be simplifying here; the other article that I simplified is centered around the conservation of energy, and that simplified article does NOT cover elastic potential energy. 

Hooke’s Law is basically this formula: F = -k times x. F represents the force exerted by the spring, k represents the spring constant, and x represents how far the spring has been compressed or stretched from its resting position. There is a negative sign in the formula because the force is opposite to the direction you pull the spring in. Think about it like this: if you pull a spring to the right, then when you let go, the spring is going to shoot back to the left, hence why the negative sign is needed in the equation. 

You might also be confused what the spring constant means. The spring constant is different for all springs, but the value of the spring constant is telling you how stiff the spring is. A higher spring constant means the spring is more stiff, and vice versa. This idea makes sense mathematically too: if a spring is more stiff, you need to put in more force to stretch it out. Looking back at the equation, if the value of k increases, then force value also increases. 

That is basically Hooke’s Law simplified. In a nutshell, it is an equation that shows how springs act when you stretch or compress it. However, you should also know what elastic potential energy is because it is related to Hooke’s Law. Elastic potential energy can be called spring energy or elastic energy. The equation to calculate elastic potential energy is this: elastic potential energy = 0.5 times k times x². In this equation, k once again represents the spring constant, and x once again represents how far the spring has been stretched or compressed. When you stretch or compress a spring, you are storing elastic potential energy in that spring; the equation tells you exactly how much elastic potential energy you are storing in the spring. When you release that spring, the elastic potential energy will turn into kinetic energy because the spring now has velocity. For a better clarification on how the spring energy turns into kinetic energy, you should also read our simplified article for the law of conservation of energy.