Greenwood press
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book-20600
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- PERIODIC FUNCTIONS
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PERIMETER The outdoor running track at the Rock Norman Complex, Clemson University, contains two semicircles and two sides that are each 100 meters in length. The turns require precision marking to ensure that all athletes run the same distance in a race. PERIODIC FUNCTIONS Graphs of functions that repeat shapes are called periodic. The horizontal length of each repetition is called the period. Phenomena that are based on cir- cular motion, such as the rotation of the earth around the sun, will often result in a periodic graph. The graph below shows the hours of daylight on the fifteenth of each month for Minneapolis. The data points start with January 15th and are plotted for two years. The period for this graph is 1 year, or 12 months. The curve that has been used to approximate the data points is a sine curve, where x is the month number: Hours = 12.2 + 2.9 sin((x − 2.3) • 2π 12 ). The tilt of the earth and its rotation about the sun cause the sinusoidal pattern in hours of daylight. Because temperature in a city is dependent on hours of sun- shine, plots of the average monthly temperature of American cities will be in the form of a sine curve. Circular motion can arise from a variety of sources. The distance above ground of a passenger in a Ferris wheel produces a sine curve as the wheel rotates. Measures on a pendulum will produce periodic functions. Gravitational attraction to the moon causes tides. As the moon rotates about the earth, the heights of tides will produce a periodic function. Sound, radar, light, radio, and ocean waves are periodic. When you press middle A on a piano, the piano strings vibrate, producing sound waves that have a period of 1/440 second. An oscilloscope provides a video screen for viewing different electrical patterns. An EKG machine in a hospital is an oscilloscope for viewing the periodic electrical patterns from a patient’s heart. Download 1.81 Mb. Do'stlaringiz bilan baham: |
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