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Exercise:
sisetupuncertay-mode separate Using the maximum error method determine the error bounds of ycosomega t for t terr and omega omerr.

Solution:
The expected value is y cosomtimes t y The value of the argument omega t om times t omt omtpi is slightly below the maximum at pi. In this range the slope of the cosine function decreases with increasing argument. In order to get the maximum error we therefore have to take the smallest possible argument: sscymin cossscomegamin ssctmin cosleft om-aom times t-at right ymin It follows for the absolute error a_y y - sscymin y - ymin ay sisetupuncertay-mode separate round-mode uncertay round-precision The result can be written as y resultyX pm ayX If the maxima for omega and t are used instead the result is significantly smaller: sscymax cossscomegamax ssctmax cosleft om+aom times t+at right ymax Longrightarrow a_y sscymax-y ymax - y aymax
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Exercise:
sisetupuncertay-mode separate Using the maximum error method determine the error bounds of ycosomega t for t terr and omega omerr.

Solution:
The expected value is y cosomtimes t y The value of the argument omega t om times t omt omtpi is slightly below the maximum at pi. In this range the slope of the cosine function decreases with increasing argument. In order to get the maximum error we therefore have to take the smallest possible argument: sscymin cossscomegamin ssctmin cosleft om-aom times t-at right ymin It follows for the absolute error a_y y - sscymin y - ymin ay sisetupuncertay-mode separate round-mode uncertay round-precision The result can be written as y resultyX pm ayX If the maxima for omega and t are used instead the result is significantly smaller: sscymax cossscomegamax ssctmax cosleft om+aom times t+at right ymax Longrightarrow a_y sscymax-y ymax - y aymax
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absolute error, error propagation
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(2, default)
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0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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