How to find the elastic force of a spring

Springs are interesting physical objects. They exhibit what scientists call Simple Harmonic Motion(SHM). SHM simply means that the object's displacement is proportional to the restoring force of the object.



You can wrap your head around that gibberish by thinking of a spring in three separate positions.

Spring A is compressed, and so naturally you would expect it to push outwards. Spring B is just sitting there, in that weird equilibrium state(no net force in any direction). Spring C is extended, so you'd expect a force pulling it back in. Do you see the connection? There exists a point where the spring is neither retracting nor extending. This point is the so-called goal of the spring. If it's extended past it, it will retract towards it, and if it's compressed beyond it, it will extend towards it.

Now here's the interesting part: the greater the distance from this magical equilibrium point, the greater the force that's applied towards the opposite direction. Opposite direction? What I mean is opposite of the direction of the displacement (the distance that it moved). So if you stretch the string out north, it wants to pull back south.

So what exactly is the effect on the elastic force of say.. 5 meters? 10 meters? How do you know the difference? We know it's linear (AKA proportionate) so it's not going to exponentially increase. But by how much?

The answer is within what is called the Spring Constant. The Spring Constant is written as Newtons per meter. What it represents is the amount of force required to compress or extend the spring 1 meter. It is the stiffness of the spring. The higher the number, the stiffer the spring.

So if we're given a displacement (the amount we pulled or pushed the spring) we can multiply this by the spring constant and vola! We have a force. This force is the amount we are putting into the spring to get it to it's current displacement. We know the spring is pulling back equally this amount because it's not moving from this position. Therefore, we know that this force is the Elastic Force of the spring!

Here is the equation:

F = -kx

K is the spring constant, and X is the displacement. We put a negative sign there because the force is equal and opposite to the product of K and X.

Cool huh?