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.
1 answer:
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Answer:
The new distance is d = 0.447 d₀
Explanation:
The electric out is given by Coulomb's Law
F = k q₁ q₂ / r²
This electric force is in balance with tension.
We reduce the charge of sphere B to 1/5 of its initial value (=q₂ = q₂ / 5) than new distance (d = n d₀)
dat
q₁ =
q₂ =
r = d₀
In order for the deviation to maintain the electric force it should not change, so we apply the Coulomb equation for the two points
F = k q₁ q₂ / d₀²
F = k q₁ (q₂ / 5) / (n d₀)²
.k q₁ q₂ / d₀² = q₁ q₂ / (5 n² d₀²)
5 n² = 1
n = √ 1/5
n = 0.447
The new distance is
d = 0.447 d₀