<p align="right">Last Update: <font color="#4f81bd">November, 25, 2024</font></p> ## BIG IDEA - There are three parts to a pendulum: anchor, string, and mass (called a bob). A simple pendulum consists of a mass attached to a string. The mass is called a _bob_. The mass is considered to be concentrated (center of mass) and friction as well as air resistance are ignored. The force exerted by the string always acts along the y-axis. The weight of the bob can be resolved into two components. The x-component is perpendicular to the string. <font color="#f79646">Conceptual Problem</font> How does the restoring force acting on a pendulum bob change as the bob swings toward the equilibrium position? How do the bob’s acceleration and velocity change? <font color="#f79646">Pendulum Demonstration</font> ![[Pendulum.png]] ![[Simple Harmonic Motion.png]] ### Relationship to acceleration due to gravity ($g$) The period ( ) and length ( ) of the string are **directly proportional** to each other. The longer the length of the strength, the longer the period. The opposite is also correct, the shorter the length of the strength, the shorter the period. $T \propto L$ The period is **inversely proportional** to the acceleration due to gravity ($g$ ). $T \propto \frac{1}{g}$ The two proportions can be combined in the formula for the period of oscillation ($T$ ). $T=2 \pi \sqrt \frac{L}{g}$ Where $T$ is the period, $L$ is length and $g$ is the acceleration due to gravity. The period is independent of mass or amplitude. ### Forces acting on a pendulum We will draw a free body diagram; arrows represent the magnitude and direction of the forces. ![[Pendulum Forces.png]] Where $L$ is length of the string, $T$ is the tension in the string, $mg$ is the weight of the bob, the $\theta$ is the angle, and $s$ is the arc length. $T$ equals $mg cos\theta$, leaving the component $-mgsine\theta$ as the net restoring force back to the equilibrium position. Newton’s second law can be written as $F=ma$, where $a$ is the acceleration. ### Slide Deck <div style="position: relative; width: 100%; height: 0; padding-top: 56.2500%; padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden; border-radius: 8px; will-change: transform;"> <iframe loading="lazy" style="position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;" src="https://www.canva.com/design/DAGPwPIDvoI/zZo47Ir9FDCsH-3MSWvGnA/view?embed" allowfullscreen="allowfullscreen" allow="fullscreen"> </iframe> </div> Video - Solving for Period <div class="sp-embed-player" data-id="cZl6rinnwWi"><script src="https://go.screenpal.com/player/appearance/cZl6rinnwWi"></script><iframe width="100%" height="480px" style="border:0;" scrolling="no" src="https://go.screenpal.com/player/cZl6rinnwWi?width=100%&height=480px&ff=1&title=0" allowfullscreen="true"></iframe></div> ### Related Topics --- [[Home|Home]] | [[Oscillations]] | [[Periodic Motion]] | [[Simple Harmonic Motion]] | [[Waves]] | [[Module 0 Sound]] | [[Electromagnetic radiation]]