10.4 Simple Pendulum

A simple pendulum is a small mass m is attached to a string of length l. We have already found that all objects fall with the same acceleration, independent of their mass; recall that small stones and large stones and cannon balls and glass marbles all fall with the same acceleration (to the degree that we can ignore air resistance). Likewise, we find that the motion of a simple pendulum does not depend upon the mass that is swinging.

Figure 10.9 A simple pendulum is a mass m attached to a string of length l. As it swings back and forth, it undergoes simple harmonic motion.

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We find that the motion of a simple pendulum does not depend upon the mass that is swinging. What, then, determines the period of such a simple pendulum? The length of the string l and the acceleration due to gravity g determine the period

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We can calculate the period using this equation,

The length of a pendulum on a clock can be adjusted to make the clock run faster or slower. A prospector or a geologist can use a carefully calibrated pendulum and some other time keeping device, like a quartz watch, to measure the local value of the acceleration due to gravity. The acceleration due to gravity may be a little greater over a large deposit of minerals such as lead and it may be a little less over a large deposit of oil.

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