======Pendulum Period Investigation======


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**Materials: **{{$demo.materials_description}}\\
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**Safety: **{{$demo.safety_description}}\\
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**Alternative titles:** Swinging on a String
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====Summary====                   
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====Procedure====  
  - Tie a small mass (washer or metal nut) to a light string and hang it from a fixed support; measure the length from pivot to the center of the bob.
  - Pull the bob to a small angle (about 10 degrees or less) and release without pushing.
  - Use a stopwatch to time 10 full swings, then divide by 10 to find the period; record length and period.
  - Repeat for at least three different lengths, keeping the angle small each time.
  - Test mass: keep length the same but swap bobs of different mass; measure the period again.
  - Test amplitude: keep length and mass the same but release from a larger angle (about 20–30 degrees) and compare the period to the small-angle result.
  - Summarize findings and compare to the model \(T \approx 2\pi\sqrt{L/g}\) for small angles.




====Links==== 
Oscillations Demo: Pendulum - Physics Demos: 
{{youtube>h3lEyW1dVCA?}}\\

Simple Pendulum | Science Experiment - Science Projects: 
{{youtube>IKAzjiMv5_4?}}\\

📄 Swinging on a String - ncwit.org: [[https://www.teachengineering.org/lessons/view/cub_mechanics_lesson09]]\\


====Variations====
  * Map period squared versus length to show a straight-line relationship.
  * Use a smartphone timer or metronome app to reduce timing error; average several trials.
  * Build a two-pendulum setup of different lengths to demonstrate phase and beating.
  * Explore gravity dependence by comparing results with an online simulator that lets you change g.



====Safety Precautions====
  * Clear a swing zone so the bob does not strike people or objects.
  * Secure the support stand or mounting point so it cannot tip or loosen.
  * Use small, smooth masses; avoid sharp edges and do not exceed safe weights for the support.




====Questions to Consider====
  * Which variable most strongly affects the period for small angles? (String length; longer length gives a longer period following \(T \propto \sqrt{L}\).)
  * Does changing the bob mass change the period? (No, mass does not affect period for an ideal pendulum at small angles.)
  * Why should the release angle be small for the formula to work well? (The small-angle approximation makes the motion nearly simple harmonic; large angles increase the period slightly.)
  * If the length is quadrupled, what happens to the period? (It doubles, because \(T \propto \sqrt{L}\).)
  * Where do engineers use pendulums today? (Timing in clocks, tuned mass dampers in buildings, seismology instruments, inertial sensors, and balance systems for robots.)