Problem 5(25%): Consider an elastic membrane stretched across a rectangular frame, to which it is fixed....
. (40 points: A membrane is stretched under tension r with uniform surface density o. (Small-amplitude) transverse displacements of this stretched membrane satisfy the wave equation కా - ఆ (10) Suppose the membrane is stretched in a rectangular frame lying in the plane z= 0, with side-lengths a, b. mitially stationary at all points, the membrane is struck at t-0 and thus set vibrating- 3.1. Show that e satisfies the following expression: veu)-ΣΣ..-ΣΣ Β.in may sin sin (wt] %3D (11)...
Problem 2. The ball with mass m is attached to two elastic cords each of length L. The ball is constrained to move on a horizontal, frictionless plain. The cords are stretched to a tension T When t 0, your intrepid instructor gives the ball a very small horizontal displacement x (a) Derive the equation of motion and find expressions for the natural circular frequency, the frequency, and the period of vibration. (b) For m - 2 kg, L 3...
(1 point) This problem will illustrate the divergence theorem by computing the outward flux of the vector field F x, y, z = 2ī + 4j + k across the boundary of the right rectangular prism: 1 sx <5,-2 Sys3,-33z37 oriented outwards using a surface integral and a triple integral over the solid bounded by rectangular prism. Note: The vectors in this field point outwards from the origin, so we would expect the flux across each face of the prism...
11. Consider a thin, infinitely long rectangular plate that is free of heat sources, as shown below. For a thin plate, is negligible, and the temperature is a function of x and y only. The solution for this problem is best obtained by considering scaled temperature (ie. 1-T - To, where To is the absolute temperature at T-0) variables, so that the two edges of the plate have "zero-zero" boundary conditions and the bottom of the plate is maintained at...
Problem 3. (25 points) For the cantilever beam shown below (A is a fixed reaction), take El as constant. You may assume the beam remains elastic. "x" is referenced from A moving right. 4 k/ft 12 ft (a) (4 pts). Calculate the reactions at the fixed connect (point A) (b) (4 pts). What are the Boundary Conditions for displacement (y and 0) for this beam? Where do they occur? (c) (8 pts). Develop the equation for the bending moment as...
Problem 3. Consider the following problem which governs the evolution of tem- perature in a bar of length l: du du 0<x<l, t>0, ot =^22+Yºu), og (0, ) = 0, de 10 , 1) = 0, u(x,0) = f(x) = A + 2 cos(") + 3 cos(477), where A, k and y are fixed positve constants. Recall that Neumann boundary con- ditions correspond to no heat flux through the boundaries (i.e. perfect insulation) and the term yều corresponds to internal...
Problem 10.19 Consider the frame shown in (Figure 1). Assume the support at A is fixed and C is a pin. EI is constant. Part A Determine the internal end moment MBA acting on member AB of the frame at B measured clockwise. Express your answer using three significant figures. Enter positive value if the moment is clockwise and negative value if the moment is counterclockwise. MBA = 40.8 k ft Submit Previous Answers Correct Part B Determine the internal...
I need help with problem #3, please and thank you!
Problem #2 (25 points) - The True Hanging String Shape After solving for ye(2) for the scenario in Problem #1, show that the mag- nitude of the tension in the string is given by the expression T(X) = To cosh (Como) where To = Tmin is the minimum tension magnitude in the string which occurs at the bottom point of the string, and then show that the maximum tension magnitude...
(1 point) This problem will illustrate the divergence theorem by computing the outward flux of the vector field F(x, y, z) - 2ri + 5y + 3-k across the boundary of the right rectangular prism: -3 <<6, -15y<3,-425 oriented outwards using a surface integral and a triple integral over the solid bounded by rectangular prism. Note: The vectors in this field point outwards from the origin, so we would expect the flux across each face of the prism to be...
(1 point) This problem will illustrate the divergence theorem by computing the outward flux of the vector field F(x, y, z) = Aci+ 4y + tek across the boundary of the right rectangular prism: -ISXS 4.-2 Sys7.-2 Szs 7 criented outwards using a surface Integral and a triple integral over the solid bounded by rectangular prism. Note: The vectors in this field point outwards from the origin, so we would expect the flux across each face of the prism to...