#5 4. Use error propagation to calculate (0, the error in a, h, t, and R...
6. Use error propagation to calculate δC, the error in C. s and k both have errors. C is related to s and k in the following way: sk
Use propagation of error techniques to calculate the following derived quantities with their errors. Give the derived error to two significant figures, and report the value of the derived quantity with significant figures limited to those of the error. For instance, if you obtain the value of the derived quantity as 4.9071 and the error as 0.478, you should report your answer as 4.91 ± 0.48. (a)x= 4.53, dx= 0.32, y= 34.38, dy= 0.45. Calculate 5x+ 7y. (b)x= 521.84, dx= 12.8,...
Error Propagation What is error propagation? A question in error propagation is that when we take a product of measurements we do what with the uncertainties? Should our uncertainties get bigger or smaller as they propagate through the formulas? Take a square and measure one side. What happens to the uncertainties when you calculate Area? Can this be beneficial when our product contains measurements of different units? The rule is to find the relative uncertainty in a product of measurements...
2. Evaluate these formulas to determine '(h) 1using e(0), (h), e(2h) for v(r) = exp(r) and h 1,0.5,0.25. Determine the error for these three values of h. Based on these values, what would you guess the dpendence of the error on h to be - linear, quadratic, cubic or of higher order? For this problem choose 3/4. 110pts 2. Evaluate these formulas to determine '(h) 1using e(0), (h), e(2h) for v(r) = exp(r) and h 1,0.5,0.25. Determine the error for...
1. Sketch a graph of the following function: f(t)-5(H(t) -2H(t-1)+ H(t-2)) 2. Use the definiton of the Laplace Transform to show that -5s 3. Find the inverse Laplace transform of the following: (a) T(s)-( (b) Y(s)=式 ) (劫 +3s 4. Solve the the following initial value problem: Sketch the function, f(), and the solution vit) on the same graph. 5. Solve the the following initial value problem: y" + 144y = δ(t); y(0) = 0, ช่ (0) =0
so Lemma Let a e R with aチ0, For the Lax-Wendroff method defined above, the truncation error is defined by 2h 2 Then, assuming that lalu S 1, we have for all n=0, . . . , Nt-1, i=1, ,N,, where Mttr:=max luttt(t.x), and Moor-max(uxox(t.x), and the maxima are taken over all (t,x) E [O, Tr] × [a, b, which are assumed to be finite Proof. Exercise so Lemma Let a e R with aチ0, For the Lax-Wendroff method defined...
(b) (5 pts) Unit Impulse. Suppose we have an impulse train signal h(t)-Σ δ(t-nT). Given an arbitrary signal r(t), find r(t)h(t) and (t) h(t) in terms of r(t) Show that r(t)h(t)-Σ r(nT)δ(t-nT) and r(t) * h(t)-Σ r(t-nT) (b) (5 pts) Find the Fourier Transform of r(t) (t 2n). Hint: Find wo and the Fourier series coefjicients then use the Fourier Transform property for periodic signals. (b) (5 pts) Unit Impulse. Suppose we have an impulse train signal h(t)-Σ δ(t-nT). Given...
3) Givenr"(t) = (6t + 4)+(-sint)i + (-4cos(2t))k, and r'O) = 0 and r(0) = 41 -1+k a) find r(t). 4) Givenf (x,y) = 6xły – yex-1 a) Find Vf(x,y). Show all support work! b) Find the direction of maximum increase of f(x,y) at the point (1,-1).
Error Propagation and Density of Materials I need you to finish the two columns(Don't worry about the third) in the table using the formulas in page one. Please show work 3) Use the Vernier caliper to measure the height, h, and the diameter, D, of the cylinder. Record h and D and their uncertainties, Ah and AD. 4) the graduated cylinder Use metal. the determine of to the volume how would you do this? Analysis The density of a sample...
4. (35 pts) Consider the system defined by: xit 5x1-2x2-R (1) #2-2x, +2x2 F) a) Compute the natural frequencies and the mode shapes. /dland -JS -2N5 b) Calculate the response for F(t)-F(t)-0 and initial conditions xo- e) Calculate the response for F-cosr, F,(o)-0 and initial conditions and -0. 0 d) Calculate Bi and B2 such that the system: -2x1 + 2x2-B2cos/6t does not experience resonance. 4. (35 pts) Consider the system defined by: xit 5x1-2x2-R (1) #2-2x, +2x2 F) a)...