Theory and Design for Mechanical Measurements
Theory and Design for Mechanical Measurements
6th Edition
ISBN: 9781118881279
Author: Richard S. Figliola, Donald E. Beasley
Publisher: WILEY
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Chapter 7, Problem 7.8P

A golf cart engine operates between 1,000 to 3,000 rpm. Engine vibrations are transmitted at these frequencies to the cart chassis. Accelerometer measurements are taken with the engine operating at 3,000 rpm. Estimate a proper sample size and sample rate to acquire at least 100 cycles of the signal and to minimize spectral leakage. What is the frequency resolution of your sampled signal for spectral analysis? What is the Nyquist frequency? Show your resulting amplitude spectrum (assume a unit amplitude for the time-based signal).

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A 100-Hz sine wave is sampled at a frequency of 6096 Hz. A total of 3048 points are taken. (a) What is the Nyquist frequency? (b) What is the frequency resolution.
Problem 2 Consider sampling input cosine functions, with a sample rate of 100Hz. (a) What is Nyquist Frequency in Hz? (b) What is the period associated with Nyquist Frequency? (c) During one period, how many samples are taken at the Nyquist frequency signal? (d) Give the values at the sample times when you start sampling at time zero. (e) Give the values at the sample times if you are sampling a sine function that is oscillating at Nyquist frequency. (f) Give the values at the sample times if you are sampling a cos (wyt - at times t = kT where T is the sample time interval for Nyquist frequency (the means that the cosine is shifted 45 degrees back in time compared to the original cosine, i.e. a phase delay from input to output). (g) We commented in class that if a cosine is sampled such that there are 4 or more samples in each period, then the control action based on the sampled values might be able to make some effective corrective action. If Nyquist frequency is 100Hz, what sample…
Problem 4-1: During a step function calibration, a first-order instrument is exposed to a step change of 100 units. If after 1.2 s the instrument indicates 80 units, estimate the instrument time constant. Estimate the error in the indicated value after 1.5 s. For this instrument, y (0) = 0 units; K = 1 unit/unit.

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Theory and Design for Mechanical Measurements

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