A laser vibrometer was used to measure the velocity of a point on the surface of

Question

A laser vibrometer was used to measure the velocity of a point on the surface of vibrating object. The first six points of the measurement collected with the sample rate of 20 Hz, together with the initial position, are shown in Table 2.1 and illustrated in Figure 2.1. Initially, the object's position was at -1.5 mm. a) What was the sample interval of the measurement in ms? Write your answer in the box. b) What is the Nyquist frequency for this data record? Write your answer in the box. c) Calculate and fill the missing values in Table 2.1.

Explanation / Answer

a) The sample interval of measurement is 0.05 x 1000 = 50 ms (as it is evident from the graph)

b) Nyquist frequency is half the frequency of the sampling rate, Nyquist = 20 / 2 = 10Hz

c) to fill out the missing values in the table , we will use the following formulae,

i) for calculating the final position we first calculate the distance covered (d) and then add the initial position (Xi) to the distance

X = V*t + Xi

Sample calculation for second step:

X2 = -1.1 x 0.05 + (-1.5 x10-3) = 0.0535 m = 53.5 mm

ii) to calculate the acceleration , we calculate the change in velocity and the time elapsed

i.e., a = V2 - V1 / t2 - t1

Sample calculation:

a2 = (-1.1 - 1.0) / 0.1-0.05 = -42 m/s2

Now , we use excel to fill out the table;

Time (s) Velocity (m/s) Position (mm) Acceleration (m/s2) 0 1 -1.5 0 0.05 -1.1 -56.5 -42 0.1 1.3 73.5 48 0.15 -1.6 -166.5 -58 0.2 1.4 113.5 60 0.25 -0.9 -111.5 -46

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