Consider the rod shown below, where the strain at any point x is given by: εx =1+ 2x2 Find the tip displacement δ.
Consider the rod shown below, where the strain at any point x is given by: εx =1+ 2x2 Find the tip displacement δ.
Problem 1 Consider the bar shown below with a cross-sectional area A, 1.2 m2, and Young's modulus E-200 X 109 Pa. Ifq,-0.02 m and q,-0.025 m determine the following (by hand calculation) (a) the displacement at point P., (b) the strain E and stress σ (e) the element stiffness matrix, and (d) the strain energy in the element 91 *p 20 m x,-15 m x,-23 m Problem 2. Consider a finite element with shape functions N1) and N2(Š) used to...
Find the center of mass of a thin plate of constant density δ covering the given region. The region bounded by the parabola y 2x-2x2 and the line y-2x The center of mass is (Type an ordered pair) Find the center of the mass of a thin plate of constant density δ covering the The center of the mass is located at (x,y): (Type an ordered pair, Round to the nearest hundredth) region bounded by the x-axis and the curve...
6. Consider a thin rod of length L laying on the x-axis as shown in the figure below. The charge density is non uniform and varies as λ = λ。x/L, where λ, is a constant. (a) Find the magnitude of the force on a point charge q at x-a in terms of q, λ, a, and L. (b) Show that for a » L the answer in (a) reduces to (c) What is the total charge on the rod? (d)...
Consider the following. lim 2x2 - 2x - 4 x-1 X + 1 Find the limit of the function (if it exists). (If an answer does not exist, enter DNE.) -6 Write a simpler function that agrees with the given function at all but one point. 9(x) =
A rational function is given. f(x)= 6x2+1/2x2+x-1 Find all vertical asymptotes, if any, of the graph of f. Find all horizontal asymptotes, if any, of the graph of f.
6. Consider a thin rod of length L laying on the x-axis as shown in the figure below. The charge density is nonuniform and varies as λ-λ, x/L, where λ° is a constant. (a) Find the magnitude of the force on a point charge q at x = a in terms of q, , a, and L. (b) Show that for a >> L the answer in (a) reduces to c) What is the total charge on the rod? (d)...
Consider the displacement of the spring shown in the following figure: 00000 +A The displacement x is given by: x = A cos (wt) Where . x is the displacement at a given time t • A is the maximum displacement w is the angular frequency, which is depended in the mass attached to the spring as well as to the spring constant and t stands for the time . Compute the displacement of x for the time intervals starting...
Consider a 2 m long metal rod. The temperature u(z,t) at a point along the rod at any time t is found by solving the heat equation k where k is the material property. The left end of the rod ( 0) is maintained at 20°C and the right end is suddenly dipped into snow (0°C). The initial temperature distribution in the rod is given by u(x,0)- (i) Use the substitution u(z,t) ta,t)+20-10z to reduce the above problem to a...
. (40pts) Consider a spring-mass-damper system shown below, where the input u() is displacement input at the right end of the spring k3 and x() is the displacement of mass ml. (Note that the input is displacement, NOT force) k3 k1 m2 (a) (10pts) Draw necessary free-body diagrams, and the governing equations of motion of the system. (b) (10pts) Find the transfer function from the input u() to the output x(t). (c) (10pts) Given the system parameter values of m1-m2-1,...
A brass rod, 1 cm in diameter and 15 cm long, with a tip subject to a breeze with a convection coefficient of 68 W/m2 K in a room where the ambient air temperature is 23°C. The base is 79°C and the tip is designed to maintain a constant temperature of 29°C. The manufacturer finds that the thermal conductivity, in units of W/m*K, to be k(T) 43*In(T)- 128, where T is in units of Kelvin. Plot the temperature profile for...