pendulum and spring period/frequency

Author: kevinlinxc

README.md

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content/formulas/hookes-law-springs/index.md

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 title: Hooke's Law (Spring Constant)
 description: Hooke's Law and the Spring Constant relate the force and displacement of a spring.
 summary: Hooke's Law and the Spring Constant relate the force and displacement of a spring.
-tags: ["physics", "mechanical engineering", "materials engineering"]
+tags: ["physics", "mechanics"]
 date: 2022-12-30
 latex: F = -kx
 ---

content/formulas/pendulum-frequency-period/index.md

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+---
+title: Pendulum Period/Frequency
+description: "The formula for the period and frequency of a simple pendulum."
+summary: "The formula for the period of a simple pendulum."
+tags: ["physics", "mechanics"]
+date: 2025-01-04
+latex: T_p = 2 \pi \sqrt{\frac{\ell}{g}}
+---
+
+{{< katex >}}
+
+The formula for the period of a simple pendulum is:
+
+$$ T_p = 2 \pi \sqrt{\frac{\ell}{g}} $$
+
+Where
+
+* \\(\small T_p\\) is the period of oscillation,
+* \\(\small \ell\\) is the length of the pendulum, and
+* \\(\small g\\) is the acceleration due to gravity.
+
+The frequency of oscillation is the reciprocal of the period:
+
+$$ f_p = \frac{1}{2 \pi} \sqrt{\frac{g}{\ell}} $$
+
+Where
+
+* \\(\small f_p\\) is the frequency of oscillation.
+
+**Note:** These formulas use an approximation that assume small oscillations (small angles) and neglects air resistance, damping, and the mass of the string.
+
+## Sources
+
+- [LibreTexts Physics](https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/Book%3A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)/15%3A_Oscillations/15.05%3A_Pendulums)

content/formulas/pendulum-frequency-period/preview.png

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+---
+title: Spring Period/Frequency
+description: "The formula for the period and frequency of a spring in simple harmonic motion."
+summary: "The formula for the period and frequency of a spring in simple harmonic motion."
+tags: ["physics", "mechanics"]
+date: 2025-01-03
+latex: T_s = 2 \pi \sqrt{\frac{m}{k}}
+---
+
+{{< katex >}}
+
+The formula for the period of a spring in simple harmonic motion is:
+
+$$ T_s = 2 \pi \sqrt{\frac{m}{k}} $$
+
+Where
+
+* \\(\small T_s\\) is the period of oscillation,
+* \\(\small m\\) is the mass attached to the spring, and
+* \\(\small k\\) is the spring constant of the spring.
+
+The frequency of oscillation is the reciprocal of the period:
+
+$$ f_s = \frac{1}{2 \pi} \sqrt{\frac{k}{m}} $$
+
+Where
+
+* \\(\small f_s\\) is the frequency of oscillation.
+
+## Sources
+
+- [HyperPhysics](http://hyperphysics.phy-astr.gsu.edu/hbase/shm2.html)

content/formulas/spring-frequency-period/index.md

@@ -31,7 +31,7 @@ def normalize_image(img_path, height, width):
         new_width = int(new_height * aspect_ratio)
 
     # Scale down the image while preserving the aspect ratio
-    scaled_image = image.resize((new_width, new_height), Image.ANTIALIAS)
+    scaled_image = image.resize((new_width, new_height), Image.LANCZOS)
 
     # Create a new blank image with the desired dimensions
     new_image = Image.new("RGB", (width, height), "white")