--- title: Simple Pendulum slug: simple-pendulum-deb55 url: /detay/simple-pendulum-deb55 type: article language: English entity: primary: Simple Pendulum type: article disambiguation: Simple Pendulum: Understand its oscillatory motion, period, and energy transformation with this concise guide. categories: - name: Machinery, Robotics And Mechatronics slug: makine-robotik-ve-mekatronik url: /kategori/makine-robotik-ve-mekatronik - name: Materials Science, Metallurgy And Ores slug: malzeme-bilimi-metalurji-ve-maden url: /kategori/malzeme-bilimi-metalurji-ve-maden - name: Defense Industry Technologies slug: savunma-sanayi-teknolojileri url: /kategori/savunma-sanayi-teknolojileri tags: - Equation of Motion - Energy Transformation - Periodic Motion - Oscillatory Motion - Pendulum author: Elyesa Köseoğlu created_at: 2025-07-20T23:45:39.101505+03:00 updated_at: 2025-07-24T09:21:58.486634+03:00 --- # Simple Pendulum ## Article Content A [simple pendulum](/en/detay/what-is-a-simple-pendulum-b26f1/llms.txt) is a type of [oscillatory motion](/en/detay/mechanical-vibrations-4c704/llms.txt) in which a mass, assumed to be a point mass, is suspended from a fixed point and swings under the influence of [gravity](/en/detay/how-was-gravity-discovered-66053/llms.txt) after being displaced from its vertical equilibrium position. Typically, the pendulum consists of a mass attached to a non-elastic, massless string or rod. The oscillations are considered under the condition of small angular displacements. ### **Definition and Theoretical Background** **Periodic motion** refers to a type of motion in which an object returns to its original position at regular time intervals. The simple pendulum exhibits [periodic motion](/en/detay/simple-harmonic-motion-a8437/llms.txt). The time taken for the pendulum to complete one full cycle is called the **period** ($T_p$), and the number of cycles per unit time is called the **frequency** (f). These quantities are related by the following expression: - $f =\frac{1}{T_f}$ - $Frekans birimi: Hertz (Hz)$ - $Periyot birimi: saniye (s)$ ### **Equation of Motion** The analysis of simple pendulum motion is based on the parameters: pendulum length 𝐿 , mass 𝑚 , and gravitational acceleration 𝑔. Assuming small angular displacements, the approximation sin ⁡ 𝜃 ≈ 𝜃 sinθ≈θ (in radians) can be applied. Under this assumption, the motion is described by a second-order differential equation: - $T_p =2.\pi \sqrt[]{\frac{L}{g}}$ According to this expression, in small-angle oscillations, the period of the pendulum depends only on the length of the string and the gravitational acceleration, and does not depend on the mass of the object. ### **Energy Transformation** During the motion of a pendulum, continuous energy transformation occurs. At the lowest point of the swing, the kinetic energy reaches its maximum, while at the highest points, the [potential energy](/en/detay/what-is-energy-fdb43/llms.txt) is at its maximum. When frictional effects (such as air resistance and pivot friction) are not neglected, the amplitude of oscillation decreases over time, and the motion becomes damped. ## Academic Sources and References 1. Gebze Teknik Üniversitesi. Basit Sarkaç Deneyi. 2025. Erişim 20 Temmuz 2025. https://www.gtu.edu.tr/Files/UserFiles/90/Deney\_Foyleri/M5.pdf. 2. Süleyman Demirel Üniversitesi Mühendislik Fakültesi. Deney 3: Basit Sarkaç. 2025. Erişim 20 Temmuz 2025. https://muhendislik.sdu.edu.tr/assets/uploads/sites/287/files/deney-3-basit-sarkac-13092022.pdf. ## Related Articles - [Roll Motion (Aviation)](//detay/roll-motion-aviation-e0984/llms.txt) - [XQ-67A](//detay/xq-67a-8e032/llms.txt) - [Vertical Tail Testing](//detay/vertical-tail-testing-f2061/llms.txt) - [Drop Testing (Aviation)](//detay/drop-testing-aviation-998d2/llms.txt) - [Moment of Inertia Testing (Aviation)](//detay/moment-of-inertia-testing-aviation-599ad/llms.txt)