Learners will examine the parameters affecting the period of a pendulum.
After completing this tutorial, you will be able to complete the following:
The science of physics defines periodic motion as motion repeated in equal intervals of time. This motion can be repeatedly moving back and forth, in a circular direction, or in an orbit. The motion of the object from a starting position back to its starting position is called a cycle. The interval of time for a cycle of the motion is called a period, and its frequency is the number of cycles per unit time. For example, a metronome may have a frequency of 60 cycles per minute and a period of 1 second. Some examples of periodic motion include: a swing in motion, a bouncing ball, and the Earth in its orbit around the Sun.
Objects that are in periodic motion can be described by the following characteristics: velocity, period of motion, and amplitude of the motion. All objects in periodic motion have velocity. Period is the time it takes for an object to go back and forth. For example, to find the period of a bouncing ball, drop a ball and measure the amount of time it takes until it bounces back up. The amplitude is 1/2 the distance the object goes before moving from one side of the period to the other. The amplitude of a pendulum swing would be the distance from the bottom to the top on one side of the swing. For an object in rotation, the amplitude is the radius of the circle (1/2 the diameter).
Pendulums have special properties in regard to frequency. The frequency of a pendulum is dependent upon the length of the pendulum. In other words, the shorter the pendulum, the greater the frequency. The frequency is independent of the amplitude of the swing. Also, the frequency is independent of the pendulum's mass. Since the effect of gravitational acceleration on a falling object is independent of the mass of the object, a pendulum with a heavy mass will move at the same rate as one with a lighter mass.
Periodic motion has played an important role in history. In the 17th century, periodic motion was studied by Galileo, Newton, and Huygens. Galileo's study began when he noticed a chandelier swinging in the breeze. He studied the swinging motion and found that it took the same amount of time for the chandelier to complete one swing no matter how wide or narrow the initial movement. This meant that time could be measured by the swing of a pendulum, which is the basis of pendulum clocks. This discovery greatly improved our ability to measure time, and was needed for the establishment of several laws of science. The study of periodic motion and the pendulum helped scientists prove that the world was round, and allowed them to calculate the value of acceleration due to gravity.
|Approximate Time||20 Minutes|
|Pre-requisite Concepts||Motion, graphs|
|Type of Tutorial||Concept Development|
|Key Vocabulary||angle of release, gravitational acceleration, harmonic motion|