082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

66 Chapter 2 Engineering functions
Example2.9 Figure2.14illustratesaperiodicwaveform.Itisoftenreferredtoasatriangularwaveform
because of its shape. The form of the function is repeated every two seconds, that
is
f(t)=f(t+2)
and so the function is periodic. The period is 2 seconds, that isT = 2. Note that this
function iscontinuous.
f(t)
–2 –1 0 1 2 3 4 t
Figure2.14
The triangularwaveform is aperiodic function.
Engineeringapplication2.2
Saw-toothwaveform
Figure 2.15 illustrates asaw-tooth voltage waveform. It is called a saw-tooth waveform
because its shape is similar to that of the teeth on a saw. It has many uses in
electronicengineering.Oneusewouldbetoprovideasignaltosweepabeamofelectrons
across a cathode ray tube in a uniform way and then quickly move the beam
backtothestartagain.Thistechniqueisusedinananalogueoscilloscopeandforms
a signalfor the time base.
The form of the function isrepeated every threeseconds, that is
v(t) = v(t +3)
v(t)
1
–3 0 3
6 9 t
Figure2.15
Thesaw-tooth waveform isaperiodicfunction.