From 33538d9a5ac70b7712897e4bf900e258633b3422 Mon Sep 17 00:00:00 2001 From: shiffman Date: Sat, 11 Nov 2023 20:21:57 +0000 Subject: [PATCH] Notion - Update docs --- content/03_oscillation.html | 30 ++++++++++++++++-------------- content/08_fractals.html | 4 ++-- content/10_nn.html | 4 ++-- 3 files changed, 20 insertions(+), 18 deletions(-) diff --git a/content/03_oscillation.html b/content/03_oscillation.html index 8733354e..b6baaf97 100644 --- a/content/03_oscillation.html +++ b/content/03_oscillation.html @@ -703,10 +703,12 @@

Exercise 3.12

Spring Forces

It’s been lovely exploring the mathematics of triangles and waves, but perhaps you’re starting to miss Newton’s laws of motion and vectors. After all, the core of this book is about simulating the physics of moving bodies. In the “Properties of Oscillation” section, I modeled simple harmonic motion by mapping a sine wave to a range of pixels on a canvas. Exercise 3.6 asked you to use this technique to create a simulation of a bob hanging from a spring with the sin() function. That kind of quick-and-dirty, one-line-of-code solution won’t do, however, if what you really want is a bob hanging from a spring that responds to other forces in the environment (wind, gravity, and so on). To achieve a simulation like that, you need to model the force of the spring using vectors.

I’ll consider a spring to be a connection between a movable bob (or weight) and a fixed anchor point (see Figure 3.11).

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- Figure 3.11: A spring with an anchor and bob. -
Figure 3.11: A spring with an anchor and bob.
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+ Figure 3.11: A spring with an anchor and bob. +
Figure 3.11: A spring with an anchor and bob.
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The force of the spring is a vector calculated according to Hooke’s law, named for Robert Hooke, a British physicist who developed the formula in 1660. Hooke originally stated the law in Latin: “Ut tensio, sic vis,” or “As the extension, so the force.” Think of it this way:

The force of the spring is directly proportional to the extension of the spring.

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The Pendulum

Solving for F_{gx}, I get:

F_{gx} = F_g \times \sin(\theta)

I’ll now rename this force F_p for “force of the pendulum.” In Figure 3.18, I’ve restored the diagram to its original orientation and relabeled the components. I’ve also moved the starting point of F_p from the bottom of the right triangle to the bob’s center, to clarify how this force moves the bob.

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- Figure 3.18: F_{gx} is now labeled F_p, the net force in the direction of motion. -
Figure 3.18: F_{gx} is now labeled F_p, the net force in the direction of motion.
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+ Figure 3.18: F_{gx} is now labeled F_p, the net force in the direction of motion. +
Figure 3.18: F_{gx} is now labeled F_p, the net force in the direction of motion.
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There it is. The net force of the pendulum that causes the rotation is calculated as follows:

F_p = F_g \times \sin(\theta)

Lest you forget, however, my goal is to determine the angular acceleration of the pendulum. Once I have that, I’ll be able to apply the rules of motion to find a new angle \theta for each frame of the animation:

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Exercise 3.15

Exercise 3.16

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Using trigonometry, how do you calculate the magnitude of the normal force depicted here (the force perpendicular to the incline on which the sled rests)? You can consider the magnitude of F_\text{gravity} to be a known constant. Look for a right triangle to help get you started. After all, the normal force is equal and opposite to a component of the force of gravity. If it helps to draw over the diagram and make more right triangles, go for it!

diff --git a/content/08_fractals.html b/content/08_fractals.html index 2888d16b..181ea5f6 100644 --- a/content/08_fractals.html +++ b/content/08_fractals.html @@ -14,8 +14,8 @@

Chapter 8. Fractals

- photo by Saad Akhtar CC BY-SA 4.0 -
photo by Saad Akhtar CC BY-SA 4.0
+ Photo by Saad Akhtar CC BY-SA 4.0 +
Photo by Saad Akhtar CC BY-SA 4.0

Chakri Maha Prasat Hall

The Chakri Maha Prasat Hall, located within the Grand Palace in the heart of Bangkok, Thailand, is an architectural feat known for its intricate details and grandeur. Each level of the multilayered roof echoes a smaller or larger version of itself and represents the different levels of Mount Meru, the center of the Buddhist universe.

diff --git a/content/10_nn.html b/content/10_nn.html index 7edcd69d..b3c9943d 100644 --- a/content/10_nn.html +++ b/content/10_nn.html @@ -8,8 +8,8 @@

Chapter 10. Neural Networks

- photo by Pi3.124, Museo Machu Picchu, Casa Concha, Cusco, CC BY-SA 4.0 -
photo by Pi3.124, Museo Machu Picchu, Casa Concha, Cusco, CC BY-SA 4.0
+ Photo by Pi3.124, Museo Machu Picchu, Casa Concha, Cusco, CC BY-SA 4.0 +
Photo by Pi3.124, Museo Machu Picchu, Casa Concha, Cusco, CC BY-SA 4.0

Khipu

The khipu (or quipu) is an ancient Incan device used for record-keeping and communication. It relied on a complex system of knotted cords to encode and transmit information. Made from colored threads and a variety of knots, each string and knot pattern represented specific data, such as census records or calendrical information. Interpreters, known as quipucamayocs, acted as a kind of accountant and decoded the stringed narrative into understandable information.