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Consider a measurement xo to where the fractional uncertainty = o/xo. Use propagating uncertainties general formula...
The general formula for propagating uncertainties to a variable ?(?, … , ?) that is a...
The general formula for propagating uncertainties to a variable ?(?, … , ?) that is a function of one or more variables is given by: ?? = √( ?? ?? ??) 2 + ⋯ + ( ?? ?? ??) 2 a. Use this general formula to derive the uncertainty propagation rule for the multiplication of two variables: if: ? = ? · ? then ( ?? ? ) ? = ( ?? ? ) ? + ( ?? ? )...
Review of Measurement Uncertainty Calculations Here are the rules for propagating uncertainties through a calculation Addition:...
Review of Measurement Uncertainty Calculations Here are the rules for propagating uncertainties through a calculation Addition: z m x + y δ,: 8x + 6y This works for any nunter of terms Subtraction:zx-y o&x + 5y This also works for any number of terns Multiplication by an exact value: z kx 82-kEx General multiplication/division: z-xy or z-:-a-Irl ) (This works for any number of factors) Exact power: z r-δε-121k] sine function: Z t, sin χ-82 tt lcos xlsr Cosine function...
(Aya2(Ayx) The propagation of uncertainty formula for the equation y-ax*2 is where Δγ,-(ax2)-((a+5a)x2)and Δγ,-(ax2)-(a(x+5x)2) and. The values δα and5x are the uncertainties on a and x respectively....
(Aya2(Ayx) The propagation of uncertainty formula for the equation y-ax*2 is where Δγ,-(ax2)-((a+5a)x2)and Δγ,-(ax2)-(a(x+5x)2) and. The values δα and5x are the uncertainties on a and x respectively. If a -35*/-0.2 and x -0*/-0.4 then what is the uncertainty on y? QUESTION 17 The propagation of uncertainty formula for the equation y-mx rb is V(Aym)2(Ay)+(Avb) where ym-(mx + b) _ ((m+5m)x + b). Дух-(mx + b)-(m(x+5x) + b) and Дуь-(mx + b)-(mx + (b +5b)) The values m 5x and b...
QUESTION 16 1 points Save Answer The propagation of uncertainty formula for the equation y-mx b is V(Aym)2+(Ay(Ayb) where Yn-(mx + b) _ ((m + &n)x + b). Дух-(mx + b) _ (m(x + 5x) + b) and 5x and...
QUESTION 16 1 points Save Answer The propagation of uncertainty formula for the equation y-mx b is V(Aym)2+(Ay(Ayb) where Yn-(mx + b) _ ((m + &n)x + b). Дух-(mx + b) _ (m(x + 5x) + b) and 5x and Sb are the uncertainties on m. x and b respectively. Ifm-o/- 0.3. x - -4.8-0.5 and b - 16/-0g then what is the uncertainty on y? O-(mx + b) _ (mx + (b + Sb)). The values 5m, QUESTION 17...
The propagation of uncertainty formula for the equation y-mx-b is/ Aym)2 + ( (Дуь) where ym-(mx + b)-((m + &m)x + b). Дух-(mx + b)-(m(x + 5x) + b) and ΔΥο (mx + b) _ (mx + (b + δb). The values &a...
The propagation of uncertainty formula for the equation y-mx-b is/ Aym)2 + ( (Дуь) where ym-(mx + b)-((m + &m)x + b). Дух-(mx + b)-(m(x + 5x) + b) and ΔΥο (mx + b) _ (mx + (b + δb). The values &m·5x and 5b are the uncertainties on m. x and b respectively. If m -39/- 0.5.x-0.2/-0.5 and b 1.5*/-o.6 then what is the uncertainty on y?
The propagation of uncertainty formula for the equation y-mx-b is/ Aym)2 +...
the whole thing. I think I figured out the first part, just having trouble with second...
the whole thing. I think I figured out the first part,
just having trouble with second part. I am not sure that they
correlate to one another.
PROPAGATING UNCERTAINTY - MULTIPLICATION AND DIVISION To learn how to propagate uncertainty when dividing, read the following example: EXAMPLE 2: You are trying to determine the speed of a person who is running. You measure the distance they run to be x = 80.0 m and the time it took them to be...
D. We will use pinv function to find a linear regression model to map the measurement data to tru...
d. We will use pinv function to find a linear regression model to map the measurement data to truth data. Our model will be Y-AX. Y is the truth data matrix Y [ yı; y2i yai ya; ysi yg: y7 ]. A is the tmeasurement data matrix A=[ 1 mh; 1 m2. 1 mai 1 m4; 1 ms: 1 mt 6:1 m7 I . and X-[Xo: x1] is the coefficient of your regression model. Truth Data yn -1 0 Measurement...
Q6. Error Analysis: Suppose that we determine F by measuring m,r,ro, and I, for the experimental...
Q6. Error Analysis: Suppose that we determine F by measuring m,r,ro, and I, for the experimental setup shown in Fig. 1.1. - C To do this, we use the formula: F - mgri – ro) = mgr1 . (1.4) If m = m + Am, ro = ro + Aro,r1 = t1 = Arı, and l = 7 + Al, show that the fractional uncertainty, F., in the calculated Fc can be expressed as: FC = |(97) + comode #camos?...
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr whic...
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr which requires n function evaluations at equidistant quadrature points and where the first and the last quadrature points coincide with the integration bounds a and b, respectively. 10pts 2. For a given v(r) with r E [0,1] do a variable transformation g() af + β such that g(-1)-0 and g(1)-1. Use this to transform the integral に1, u(z)dz to an...
LEl equation. 8. Consider the equation y" + xy' + y = o. a. Pind its general solution y E cnx in the form y Ayx)By2) where y1 and y2 are power series b. Use the ratio test to verify that...
LEl equation. 8. Consider the equation y" + xy' + y = o. a. Pind its general solution y E cnx in the form y Ayx)By2) where y1 and y2 are power series b. Use the ratio test to verify that the two series y, and yp converge for all x. Write out the theozn in the book both series would converge. 2 , and use this fact c. Show that y,(x) is the series expansion of e , to·ind...
Review of Measurement Uncertainty Calculations Here are the rules for propagating uncertainties through a calculation Addition: z m x + y δ,: 8x + 6y This works for any nunter of terms Subtraction:zx-y o&x + 5y This also works for any number of terns Multiplication by an exact value: z kx 82-kEx General multiplication/division: z-xy or z-:-a-Irl ) (This works for any number of factors) Exact power: z r-δε-121k] sine function: Z t, sin χ-82 tt lcos xlsr Cosine function...
(Aya2(Ayx) The propagation of uncertainty formula for the equation y-ax*2 is where Δγ,-(ax2)-((a+5a)x2)and Δγ,-(ax2)-(a(x+5x)2) and. The values δα and5x are the uncertainties on a and x respectively. If a -35*/-0.2 and x -0*/-0.4 then what is the uncertainty on y? QUESTION 17 The propagation of uncertainty formula for the equation y-mx rb is V(Aym)2(Ay)+(Avb) where ym-(mx + b) _ ((m+5m)x + b). Дух-(mx + b)-(m(x+5x) + b) and Дуь-(mx + b)-(mx + (b +5b)) The values m 5x and b...
QUESTION 16 1 points Save Answer The propagation of uncertainty formula for the equation y-mx b is V(Aym)2+(Ay(Ayb) where Yn-(mx + b) _ ((m + &n)x + b). Дух-(mx + b) _ (m(x + 5x) + b) and 5x and Sb are the uncertainties on m. x and b respectively. Ifm-o/- 0.3. x - -4.8-0.5 and b - 16/-0g then what is the uncertainty on y? O-(mx + b) _ (mx + (b + Sb)). The values 5m, QUESTION 17...
The propagation of uncertainty formula for the equation y-mx-b is/ Aym)2 + ( (Дуь) where ym-(mx + b)-((m + &m)x + b). Дух-(mx + b)-(m(x + 5x) + b) and ΔΥο (mx + b) _ (mx + (b + δb). The values &m·5x and 5b are the uncertainties on m. x and b respectively. If m -39/- 0.5.x-0.2/-0.5 and b 1.5*/-o.6 then what is the uncertainty on y?
The propagation of uncertainty formula for the equation y-mx-b is/ Aym)2 +...
the whole thing. I think I figured out the first part,
just having trouble with second part. I am not sure that they
correlate to one another.
PROPAGATING UNCERTAINTY - MULTIPLICATION AND DIVISION To learn how to propagate uncertainty when dividing, read the following example: EXAMPLE 2: You are trying to determine the speed of a person who is running. You measure the distance they run to be x = 80.0 m and the time it took them to be...
d. We will use pinv function to find a linear regression model to map the measurement data to truth data. Our model will be Y-AX. Y is the truth data matrix Y [ yı; y2i yai ya; ysi yg: y7 ]. A is the tmeasurement data matrix A=[ 1 mh; 1 m2. 1 mai 1 m4; 1 ms: 1 mt 6:1 m7 I . and X-[Xo: x1] is the coefficient of your regression model. Truth Data yn -1 0 Measurement...
Q6. Error Analysis: Suppose that we determine F by measuring m,r,ro, and I, for the experimental setup shown in Fig. 1.1. - C To do this, we use the formula: F - mgri – ro) = mgr1 . (1.4) If m = m + Am, ro = ro + Aro,r1 = t1 = Arı, and l = 7 + Al, show that the fractional uncertainty, F., in the calculated Fc can be expressed as: FC = |(97) + comode #camos?...
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr which requires n function evaluations at equidistant quadrature points and where the first and the last quadrature points coincide with the integration bounds a and b, respectively. 10pts 2. For a given v(r) with r E [0,1] do a variable transformation g() af + β such that g(-1)-0 and g(1)-1. Use this to transform the integral に1, u(z)dz to an...
LEl equation. 8. Consider the equation y" + xy' + y = o. a. Pind its general solution y E cnx in the form y Ayx)By2) where y1 and y2 are power series b. Use the ratio test to verify that the two series y, and yp converge for all x. Write out the theozn in the book both series would converge. 2 , and use this fact c. Show that y,(x) is the series expansion of e , to·ind...
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