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For small swings the pendulum approximates a harmonic oscillator and its motion as a function of time t is approximately simple harmonic motion.
1 2 1 harmonic small swings. Therefore the motion of a simple pendulum is simple harmonic. User nidem uploaded this swings pendulum simple harmonic motion oscillation harmonic oscillator small angle approximation png image on august 23 2017 608 pm. The resolution of this file is 512x501px and its file size is.
A simple pendulum is defined to have an object that has a small mass also known as the pendulum bob which is suspended from a light wire or string such as shown in figure 1. Where is a constant value dependent on initial conditions. The amount of time it takes the swing to complete its cycle depends on the length of the rope and nothing else.
The image can be used for personal use only. For small displacements a pendulum is a simple harmonic oscillator. If you make a graph of the distance the swing travels crossways with time the result is a sine wave.
Exploring the simple pendulum a bit further we can discover the conditions under which it performs simple harmonic motion and we can derive an interesting expression for its period. If the pendulum swings through a small angle and is measured in radians sin x is almost equal to x. When the arc of swing is large the swing moves quickly when the arc is small the swing moves slowly.
X m a gx a g dl a x d l radians a gl d a k d a a d the acceleration of the bob is directly proportional to the distance from the centre point.
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