Higher Engineering Mathematics, Sixth Edition

Trigonometric waveforms 151

waveform using harmonic synthesis over one

cycle of the fundamental waveform.

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⎢

⎣

(a)v=300sin314. 2 t

+90sin( 628. 3 t−π/ 2 )

+30sin( 1256. 6 t+π/ 3 )V

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3. A voltage waveform is represented by:

v= 20 +50sinωt

+20sin( 2 ωt−π/ 2 )volts.

Draw thecomplex waveform over one cycle of

the fundamental by using harmonic synthesis.

4. Write down an expression representing a
   currentihaving a fundamental component of
   amplitude 16A and frequency 1kHz, together
   withitsthirdand fifthharmonics beingrespec-
   tively one-fifth and one-tenth the amplitude
   of the fundamental, all components being
   in phase at zero time. Sketch the complex

current waveform for one cycle of the funda-

mental using harmonic synthesis.

[

i=16sin2π 103 t+ 3 .2sin6π 103 t

+ 1 .6sinπ 104 tA

]

5. A voltage waveform is described by

v=200sin377t+80sin

(

1131 t+

π

4

)

+20sin

(

1885 t−

π

3

)

volts

Determine (a) the fundamental and harmonic

frequencies of the waveform (b) the percent-

age third harmonic and (c) the percentage

fifth harmonic. Sketch the voltage waveform

usingharmonic synthesis over one cycle of the

fundamental. ⎡

⎢

⎣

(a)60Hz,180Hz,300Hz

(b)40%

(c)10%

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