Please Use Given Formulas 1 (29.32 KiB) Viewed 24 times
Q1. A force sensor is to be selected to measure a time-dependent force. Based on the information provided. by the manufacturer the dynamics of the force sensor can be modeled as: ÿ + 0.4 y + 0.12y = F(t) If F(t) = 2 +15sin(0.5t): (a) Obtain the time constant of the force sensor. (4 Pts.) (b) Determine the dynamic error of the force sensor when it is used to do measurements at the ringing frequency. (8 Pts.) (c) Calculate the phase shift of the force sensor when it is used to measure accelerations with frequencies equal to half of the resonance frequency of the accelerometer. (8 Pts.) (d) Calculate the steady output of the force sensor. (8 Pts.)
a₂y+ay+aoy = F(t) a do (= W a2 2√apa₂ 1+ (2π/In(2/₂))² T = 1/5W, M() = 1/2 {[1 - (09/0₂)²] + [20/0,1²} 250/0, 1-(w/w)² = B(w) ΚΑ (o)= tan WR Wn1 √√1-28² 1 Vrms 1₂-1₁ +=√₁. -f₁[y] di @d +²y+y=KF(t) @n 1 12-115 8(w) = M(w) - 1 Ystrady (1)=y(1-x) = B(w)sin[oor + Þ(c)] y fy(1) dt
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