Page 28 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Chap. 1 Problems 15

1-12 Determine the Fourier series for the sawtooth curve shown in Fig. Pl-12. Express the
result of Prob. 1-12 in the exponential form of Eq. (1.2-4).

Figure Pl-12.

1-13 Determine the rms value of a wave consisting of the positive portions of a sine wave.
1-14 Determine the mean square value of the sawtooth wave of Prob. 1-12. Do this two
ways, from the squared curve and from the Fourier series.
1-15 Plot the frequency spectrum for the triangular wave of Prob. 1-11.
1-16 Determine the Fourier series of a series of rectangular pulses shown in Fig. Pl-16. Plot
:
c„ and versus n when A = |.
1.0

— kir
Figure Pl-16.

1-17 Write the equation for the displacement s of the piston in the crank-piston mechanism
shown in Fig. Pl-17, and determine the harmonic components and their relative
magnitudes. If r/I = what is the ratio of the second harmonic compared to the
first?

Figure Pl-17.
1-18 Determine the mean square of the rectangular pulse shown in Fig. PI-18 for k = 0.10.
If the amplitude is A, what would an rms voltmeter read?
A 1 ____ 1____
1
1
1
1 1
1 1
____1____ 1
I
^ ------ r -------- Figure Pl-18.
1-19 Determine the mean square value of the triangular wave of Fig. Pl-11.
1-20 An rms voltmeter specifies an accuracy of ±0.5 dB. If a vibration of 2.5 mm rms is
measured, determine the millimeter accuracy as read by the voltmeter.
1-21 Amplification factors on a voltmeter used to measure the vibration output from an
accelerometer are given as 10, 50, and 100. What are the decibel steps?