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

(Steven Felgate) #1

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


Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).

圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀

Free download pdf