Question Solved1 Answer 3.12 Determine the frequency response [Mw) and (w)] for an instrument having a time constant of 10 ms. Estimate the instrument's usable frequency range to keep its dynamic error within 10%.

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Transcribed Image Text: 3.12 Determine the frequency response [Mw) and (w)] for an instrument having a time constant of 10 ms. Estimate the instrument's usable frequency range to keep its dynamic error within 10%.
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Transcribed Image Text: 3.12 Determine the frequency response [Mw) and (w)] for an instrument having a time constant of 10 ms. Estimate the instrument's usable frequency range to keep its dynamic error within 10%.
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Solution: Given data: Time constant&#160;tau=10ms=0.01s Delta= Error <= +-10% F(t)=A sin omega t (Assume) rarr Input For first order system; M(omega)=(1)/(sqrt(1+(0.01 omega)^(2))^(2)) phi(omega)=-tan^(-1)(0.01 omega) M(omega) phi(omega) 1 1 -0.573^(@) 10 0.995 -5.71^(@) 100 0.7071 -45^(@) 1000 0.0995 -84.289^(@) &#160; when&#160;omega=tau =>M(omega)=0.7071 For first o ... See the full answer