2 Math Compute the following: 1. 2.5 * 10-15 2. π-2 - 3. 6(4-2)3 3(4) 4. 3cos (T)-78 25 еп-1 5. 4 π2+2

Use the graphical method to solve the problem

J 1. Using Lagrangian mechanics, derive the equations of motion of a cart with two tires under the cart shown in Figure P.4.1.

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I am trying to derive the Jacobian matrix, the J_J2 in the image. Can you help me calculate the partial derivatives?

4. Consider the following system 0 3 -1 [ 1 ¦ ] * ) + [ ³ } } } ] × 0) = 0 4 where M is in [kg] and K is in [N/m]. (t) a. Calculate the eigenvalues of the system. -1 b. Calculate the eigenvectors and normalize them. 1 (t)

ll b) Obtain the mathematical model of the system shown in Figure Q2b using Newton's second law of motion, F=ma. k₁ w 3- 777777 C1 7771 k₂ D 7777 Figure: Q2b Page 2 of 7 A C2 1112

A square domain is modeled using either one bilinear rectangular element or two linear triangular elements as shown below. a) Determine the system element matrix for the Laplace equation for each discretization. b) Determine the displacement at the center of the domain (0.5,0.5) in terms of the nodal displacement. Hint: You need to assemble the stiffness matrix for the system on the right to form a 4*4 matrix from the two 3*3 element matrices. 1.0 4. 1.0 3. X- 1.0 1.0 2. 2.

Please i need her solve all choose

please answer question 3 , 5, 7 in full detail explanation