Problem 2: Drive the weak form on the interval [a.b] for assuming α is a constant that would prod...
(40 pts) 2a. Show that u(z) is the solution to the problem where k(x)-1 for x < 1/2 and k = 2 for x > 1 /2. 2b. Set up the weak form for the differential equation above and the resulting element stiffness and element load vector and calculate the element stiffness matrix and load vector for 4 quadratic elements by using the Gaussian quadrature that is going to exactly calculate the integrals Then set up the global K and...
Α'2 = Σ Λ Α' (4.4) V=1...2 The instructions under the summation symbol tell us to assign the values t, x, y, z to the index v and sum the four terms that result. The value of u is left unspecified: if = 1, then this equation corresponds to the first row of equation 4.1; if u = x, it corresponds to the second line of 4.1, and so on. Equations 4.4 and 4.1 are equivalent. Equation 4.4 can be...
Problem 2 [Required]: For the truss below (and using the Stiffness Method): (a) Determine the global stiffness matrix; (b) Calculate the vertical and horizontal displacement at joint B; (c) Calculate the force in members 1 and 5; (d) Calculate the reaction forces. NOTE: Joint A is pinned and Joint D is a roller. AE is constant. Use the chart below for selecting near and far nodes and use the provided coordination numbers. u2 2m 5 2 kN 3 Element 2...
Problem 2 Given the 2-DoF PR robot shown, assuming no friction, link 1's center of mass is at its middle ( ½ L), and link 2's center of mass is 1/3L from the proximal end, imz (a) Derive the equations of motion in variable form to find the joint torques/forces F, and τ2-write answers below. b) Express the equations in matrix form using the formulation Clearly indicate each term in the matrices 0.2 .92 . π rad, θ2-0.1 rad, θ.....
Consider the initial value problem: 2' - 2+ 2(0) = (*) a. Form the complementary solution to the homogeneous equation. -e (t) = 21 +02 b. Construct a particular solution by assuming the form zp(t) = ae+ bt+c and solving for the undetermined constant vectors a, b, and c. 2p(t) = c. Solve the original initial value problem. 31(t) ) - 22(0)
Figure 3. Double delta-function potential. X +a V(x) 2. Consider the symmetric, attractive double delta function potential illustrated in Fig. 3 where α is a positive constant. There are two lengths in this problem, the separation between the delta functions, 2a, and the decay lengthK-1-쁩)" of the wave function for an attractive delta function potential. [Note: In this problem, you may not need much math, but explain clearly the reasoning for your answers.] (a) How many bound states do you...
Problem 1: We are interested in solving a modified form of diffusion equation given below using Fourier transforms au(x,t) The domain of the problem is-oo < x < oo and is 0 < t < oo . At time t = 0, the initial condition is given by u (x,0)-0 a) Take the Fourier transform on x and show that the above PDE can be transformed into the following ODE where G() is the Fourier transform of g(x) and U(w,...
Previous Problem Problem List Next Problem (1 point) Let's find the general solution to z2y"-5zy, + 8y-(2-P) using reduction o of order (1) First find a non-trivial solution to the complementary equation z' smaller power m. 5zy' +8y0 of the form z. There are two possibilities, pe (2) Now set u = tizm and determine a first order equation (in standard form) that ,' t' must satisfy (3) Solve this for z using cl as the arbitrary constant 4) Solve...
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Assuming that other factors are held constant, which of the following would tend to increase the likelihood of rejecting the null hypothesis? Decrease the sample size Increase the sample mean difference Increase the sample variance None of the other 3 options would increase the likelihood Which of the following is the correct null hypothesis for a repeated-measures t test? MD 0 M1 M2 One sample of n=8 scores has a variance of s 6 and a second...
Assuming that the population is normally distributed, construct a 99% confidence interval for the population mean for each of the samples below. Explain why these two samples produce different confidence intervals even though they have the same mean and range. Sample A: 1 3 3 4 5 6 6 8 Sample B: 1 2 3 4 5 6 7 8 Full data set Construct a 99% confidence interval for the population mean for sample A (Type integers or decimals rounded...