A second order measuring system has a known natural frequency of 2000 Hz and damping ratio of 0.8. Would it be satisfactory to u
se it to measure a signal expected to have frequency content at up to 500 Hz? Demonstrate your answer by finding the expected dynamic error and phase shift at 500 Hz.
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Answer:
a) F = 680 N, b) W = 215 .4 J , c) F = 1278.4 N
Explanation:
a) Hooke's law is
F = k x
To find the displacement (x) let's use the elastic energy equation
= ½ k x²
k = 2 / x²
k = 2 85.0 / 0.250²
k = 2720 N / m
We replace and look for elastic force
F = 2720 0.250
F = 680 N
b) The definition of work is
W = ΔEm
W = -
W = ½ k ( ² - x₀²)
The final distance
= 0.250 +0.220
= 0.4750 m
We calculate the work
W = ½ 2720 (0.47² - 0.25²)
W = 215 .4 J
We calculate the strength
F = k
F = 2720 0.470
F = 1278.4 N