B2/B3 - Thursday - Pendulum Reading

Part 1: Reading for Main Idea   Purpose: What causes a pendulum to move? What factors affect the motion of a pendulum?   A few definitions before you start:             Oscillation – a motion of moving back and forth at a regular interval             Period – the amount of time needed for one full oscillation; the time for an oscillating object to return to its start   Pendulum Measurements Another method by which we can measure the acceleration due to gravity is to observe the oscillation of a pendulum, such as that found on a grandfather clock. Contrary to popular belief, Galileo Galilei made his famous gravity observations using a pendulum, not by dropping objects from the Leaning Tower of Pisa. If we were to construct a simple pendulum by hanging a mass from a rod and then displace the mass from vertical, the pendulum would begin to oscillate about the vertical in a regular fashion. The relevant parameter that describes this oscillation is known as the period (time to make one full swing) of oscillation.                    The reason that the pendulum oscillates about the vertical is that if the pendulum is displaced, the force of gravity pulls down on the pendulum. The pendulum begins to move downward. When the pendulum reaches vertical it can't stop instantaneously. The pendulum continues past the vertical and upward in the opposite direction. The force of gravity slows it down until it eventually stops and begins to fall again. If there is no friction where the pendulum is attached to the ceiling and there is no wind resistance to the motion of the pendulum, this would continue forever.                     Because it is the force of gravity that produces the oscillation, one might expect the period of oscillation to differ for differing values of gravity. In particular, if the force of gravity is small, there is less force pulling the pendulum downward, the pendulum moves more slowly toward vertical, and the observed period of oscillation becomes longer. Thus, by measuring the period of oscillation of a pendulum, we can estimate the gravitational force or acceleration.                    It can be shown that the period of oscillation of the pendulum, T, is proportional to one over the square root of the gravitational acceleration, g. The constant of proportionality, k, depends on the physical characteristics of the pendulum such as its length and the distribution of mass about the pendulum's pivot point (see equation to the right)                    The small variations in pendulum period that we need to observe can be estimated by allowing the pendulum to oscillate for a long time, counting the number of oscillations, and dividing the time of oscillation by the number of oscillations. The longer you allow the pendulum to oscillate, the more accurate your estimate of pendulum period will be. This is essentially a form of averaging. The longer the pendulum oscillates, the more periods over which you are averaging to get your estimate of pendulum period, and the better your estimate of the average period of pendulum oscillation.