CU-Boulder MCEN 3037 - 21R (17 pages)

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21R



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21R

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Pages:
17
School:
University of Colorado at Boulder
Course:
Mcen 3037 - Data Analysis
Data Analysis Documents

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INPUT sensor transducer Signal A MEASUREMENT SYSTEM Signal B OUTPUT Signal C How does the measurement system respond to a given Input Static signals the input measurand is unchanging in the time required to make a measurement Dynamic signals signals change over time characteristics of time dependent signals may be important parameters in the measurement The measurement system that we use must be fast enough to keep up with the input signal the dynamic frequency response is critical The primary function of a measurement system is to sense an input signal and transform this to a useable output signal m is the bulb mass C is the bulb specific heat h is the heat transfer coefficient A is the surface area How about a simple bulb thermometer the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings hA TB TW TB0 TW exp t cm t TW TB0 TW exp cm hA Zero order responds instantly to measurand no instrument is truly zero order but many can be approximated as zero order First order show capacitive type energy storage effects mechanical analogs to capacitors are springs and devices that store thermal energy thermometer is a first order system Second order have inertial effects of inductance or accelerated mass as well as capacitive effects common spring mass systems bathroom scale Second order systems include a characteristic called damping or energy loss Specifications for the dynamic response include the response to a Step input transient response and the response to a range of Sinusoidal inputs frequency response Zero order Second order input Step transient response Frequency response Sinusoidal input magnitude First order frequency We will model our measurement system as an nth order ordinary differential equation The general form is dny d n 1 y d y an n an 1 n 1 a1 ao y F t dt dt dt The coefficients are determined by the type of system we are trying to model F t is the Forcing Function and can also be generalized



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