Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

210 Chapter 8 Time and Time-Related Parameters

Mass

Spring

■Figure 8.4

A spring—mass system.

outside of our homes engaging in outdoor activities. Moreover, because more people drive dur-

ing the daylight hours, daylight saving can also reduce the number of automobile accidents, con-

sequently saving many lives.

In 1966, the U.S. Congress passed the Uniform Time Act to establish a system of

uniform time. Moreover, in 1986, Congress changed the initiation of daylight saving time from

the last Sunday in April to the first Sunday in April. In 2005, Congress approved an amend-

ment to have daylight saving time start on the second Sunday in March and end on the first Sun-

day in November, commencing in 2007. Today, most countries around the world follow some

type of daylight saving schedule. In the European Union countries, the daylight saving begins

on the last Sunday in March and continues through the last Sunday in October.

8.3 Periods and Frequencies

For periodic events, a periodis the time that it takes for the event to repeat itself. For example,

every 365.24 days the earth lines up in exactly the same position with respect to the sun. The

orbit of the earth around the sun is said to be periodic because this event repeats itself. The

inverse of a period is called a frequency. For example, the frequency at which the earth goes

around the sun is once a year.

Let us now use other simple examples to explain the difference between period and fre-

quency. It is safe to assume that most of you do laundry once a week or buy groceries once

a week. In this case, the frequency of your doing laundry or buying groceries is once a

week. Or you may go see your dentist once every six months. That is the frequency of your

dentist visits. Therefore, frequency is a measure of how frequently an event or a process

occurs, and period is the time that it takes for that event to complete one cycle. Some engi-

neering examples that include periodic motion are oscillatory systems such as shakers, mix-

ers, and vibrators. The piston inside a car’s engine cylinder is another good example of

periodic motion. Your car’s suspension system, the wings of a plane in a turbulent flight,

or a building being shaken by strong winds may also show some component of periodic

motion.

Consider a simple spring – mass system, as shown in Figure 8.4. The spring – mass system

shown could represent a very simple model for a vibratory system, such as a shaker or a

vibrator. What happens if you were to push down on the mass and then let go of it? The mass

will oscillate in a manner that manifests itself by an up-and-down motion. If you study

mechanical vibration, you will learn that the natural undamped frequency of the system is given

by

(8.1)

wherefnis the natural frequency of the system in cycles per second, or Hertz (Hz),krepresents

the stiffness of the spring or an elastic member (N/m), andmis the mass of the system (kg).

fn

1

2 p

B

k

m

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