PCS 125 LAB 1 - Objective...

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Objective The purpose of this experiment was to investigate the characteristics of the  pendulum motion and understand how different characteristics such as the mass of the  pendulum bob, amplitude of the swing, and length of the pendulum affect its period. In  order to extract these relationships, a controlled experiment was conducted with the  pendulum by changing one variable at a time and seeing how each one of the variables  (length, mass and amplitude) affected the period.    Another abstract of this experiment was to determine the difference between a simple  pendulum and a physical pendulum, and see whether their periods depend on the same  variables.  After performing different trials and taking measurements by changing only one  variable at a time and conducting a series of controlled experiments with the simple  pendulum. It was seen and concluded from the results that; Changes in the mass of the bob has no significant effect on the period  By changing the amplitude of the pendulum swing the period stays fairly constant The pendulum period is directly proportional to its length  Next, a trial was done with the physical pendulum and the period was measured and  recorded. Based on the results and the current theories it was found that the period of a  compound pendulum depends on several factors such as, Mass of the suspended body Length between the center of the mass and the suspension axis The moment of inertia
THEORY Depending on the shape of the pendulum, a pendulum can be categorized as a simple one (simple pendulum) or a compound one (physical pendulum). A simple pendulum is a mass hung vertically by a string from a fixed point in a way that it can swing freely. In a physical pendulum a rigid body is suspended from a fixed point in a way that it can move freely about its position of equilibrium. 1 When a simple pendulum is in motion (swinging) it keeps a very regular and consistent beat, and for this manner it has been used for different purposes such as, laboratories and scientific apparatus, clocks, astronomical measurements, and etc. 2 While constructing labs as such it is important that the observer records not one but five or even ten periods and calculate an average. By doing this accuracy goes up, and a lower percentage error would be received. When describing a pendulum’s motion, one of the factors to consider would be its period (T), which can be affected by the mass of the bob, length of the swing, and the amplitude of the pendulum. 3 However, current studies and theories show that the period of the pendulum depends only on the length of its swing. 4 When a pendulum is in motion as shown in figure (1), its mass (the bob of the pendulum) moves in a simple harmonic motion, where the inertia is the bob. Whenever the mass passes through the midpoint the direction of the tangential component will change and therefore restoring the mass to the central position 4. The restoring force can be calculated from the following equation:
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