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plz solve. instrumentation
Q5: FORCE AND NONLINEARITY Bentley, Part A &B An instrument which measures force is calibrated before use. Initially output signal is set to zero when there is no applied force. Full-scale value of force for this instrument is 200.0 N. A precisely known force of this value is then applied by a deadweight tester and voltage at output of the instrument is then adjusted to read exactly 5.000 V. During subsequent operation, the user assumes that the instrument has a static characteristic which is perfectly linear However, in fact, the relationship between force Fas measurand and output voltage Vis not linear and behaviour is described by a cubic polynomial equation: V = A F+BP + CP For this instrument, the three coefficients of the polynomial have the following quantitative values: A = +3.542x10-2 V N-1 B = -1.172x10-4 V N-2 C = +3.255x10-7 V N-3 Measurements are interpreted according to an invalid assumption that the characteristic is linear. Consequently inferred values of measurand are subject to nonlinearity error. Q5A) Derive an algebraic expression which describes magnitude of this nonlinearity error as a function of the value of force F. Nonlinearity error should itself be expressed as an error AF in force as measurand. Sketch this variation of error with measurand. Q5B) From algebraic expression or graph (preferably the former), determine maximum value of nonlinearity error within the working range of the instrument. (ANS = +10.9 N) Q5C) Furthermore determine extreme values of actual sensitivity of the instrument. Compare these minimum and maximum values of sensitivity with nomin value deriv rom the calibration process. (ANS = +2.135x102 V Nito +3.542x102 V N') Q5D) Discuss how an instrument may be properly calibrated and then used for accurate measurement if static characteristic is described by a cubic equation.