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

8.3 Periods and Frequencies 211

The period of oscillation,T, for the given system — or in other words, the time that it takes for

the mass to complete one cycle — is given by

(8.2)

Most of you have seen oscillating pendulums in clocks. The pendulum is another good

example of a periodic system. The period of oscillation for a pendulum is given by

(8.3)

whereLis the length of the pendulum ( m) andgis the acceleration due to gravity ( m/s

2

).

Note that the period of oscillation is independent of the mass of the pendulum. Not too

long ago, oil companies used measured changes in the period of an oscillating pendulum to

detect variations in acceleration due to gravity that could indicate an underground oil

reservoir.

An understanding of periods and frequencies is also important in the design of electrical

and electronic components. In general, excited mechanical systems have much lower frequencies

than electrical /electronic systems. Examples of frequencies of various electrical and electronic

systems are given in Table 8.1.

T 2 p

B

L

g

T

1

fn

TABLE 8.1 Examples of Frequencies of Various Electrical

and Electronic Systems

Application Frequency

Alternating current (USA) 60 Hz

AM radio 540 kHz –1.6 MHz

FM radio 88 –108 MHz

Emergency, fire, police 153 –159 MHz

Personal computer clocks (as of year 2010) up to 3 GHz

Wireless router (2009) 5 GHz

m = 2 kg

k = 5 N/mm = 5000 N/m

■Figure 8.5 A simple spring–mass system.

Example 8.1 Determine the natural frequency of the simple spring-mass system shown in Figure 8.5.

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