I have your pie In fact, the mass, period, and spring constant can be measured separately and used to calculate pi.
However, we can also represent this oscillation using a mathematical function. This is the simplest formula that gives mass position as a function of time. where A is the amplitude of motion and ω is the angular frequency.
Illustrated by Rhett Allan
This solution contains the trigonometric cosine. If trigonometric functions are blurry, remember that all trigonometric functions tell you the ratio of the sides of a right triangle. For example, the cosine of 30 degrees says that if you have a right triangle with one 30 degree angle, you have the length of the side adjacent to this angle divided by the length of the hypotenuse. (In this case it would be 0.866).
(It may seem strange that in order to understand the motion of a spring, we need a mathematical function that is also used in triangles, but after all, this function just so happens to be our equation. In short, I We use it because it works. Anyway, stick with me.)
Now imagine that the angles of a right triangle are constantly increasing. (This is the ωt term.) Because the angle changes, we essentially have a triangle that rotates in a circle. If you look at just one side of this right triangle and see how it changes over time, that’s where the trigonometric functions are. It looks like this:
Video: Rhett Allan
Since this oscillation is related to a circle, it is clear that the pi is there.
In fact, pi can be found for other kinds of vibrations that can be modeled with trigonometric functions involving sines or cosines. Think, for example, of a pendulum, which is a mass swinging from a string, or of a diatomic molecule (a molecule with two atoms in it, like nitrogen) vibrating, or even a changing electric current like a circuit in a radio. it vibrates.
uncertainty principle
For physics buffs, perhaps the most popular fundamental wave is called the h-bar (ħ). This is basically Planck’s constant (h) divided by 2π.
The Planck constant describes the relationship between energy and frequency for very small bodies such as atoms. You can measure this constant yourself using some LEDs. In fact, pi appears so often in models dealing with small quantum matter that physicists combine pi and h to make the h bar.
