Why does the length of the period increase as the length of the pendulum increases?

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The period of a pendulum increases as it length increases because the verticle distance the bob travels is less, and thus there is less potential energy available to accelerate the bob in its arc. Also, recall that in vector mechanics the horizontal force vector due to gravity is a function of the direction the object is constrained to follow, and if the pendulum is longer, that direction is more horizontal, giving the horizontal force vector less of an effect.