Use the equivalent systems method to derive the differential equation governing the motion of the bar shown in the figure, when the bar subjected to clockwise angular displacement from the equilibrium position. Assume small and consider the translational displacement of the center of the bar. k

Use the free body diagram method to derive the differential equation governing the motion of the system show in the below figure, using as the generalized coordinate.

35 üzerinden işaretenmiş P Soruyu işarete Henüz cevaplanmadı Fss rininininn. 3) For the spring assemblage shown below Figure, obtain (a) the global stiffness matrix, (b) the displacements of nodes 2-4, (c) the global nodal forces. Node 1 is fixed while node 5 is given a fixed, known displacement 5 = 200 mm. The spring constants are all equal to k = 200 kN/m.

I In this problem, consider the figure below. A disk with radius r, mass m, and moment of inertia of Io about the point O is on an inclined plane, with the translational coordinates and y and rotation angle 0, as shown. The direction of gravity is shown, and the incline angle is a. A constant input torque is applied at the point O in the direction shown, and it is opposed by a damping torque from a bearing with value co in the direction shown. The point P represents a point of instantaneous contact, rolling without slipping. Your tasks: Direction of Gravity M(t) co 0 P x Mass: m Figure 2: System schematic. Moment of Inertia about 0: lo a: Incline Angle A Draw the FBD for the disk. B Derive the equation of motion with the rotation angle as the dynamic variable. 0 C Take the Laplace transform, and solve for (s), letting the initial conditions be 0(0) = 0 and (0) = 0. Remember that a constant is a step function for a one-sided Laplace transform. D Given your expression for (s), find the…

P4.8 Determine the rotational speed of link 3 of the mechanism given in figure P4.8 for the position shown. Use a complex numbers approach

Q1: The system shown has two masses. Beam of mass (Jo#m L² kg.m²) rotates about fixed point (O) and its free end is connected to disk rotates about fixed point (O₂). Consider all connecting links are massless and rigid. Find 1- The displacements of points A, B, and C in addition to the rotations of masses, all in terms of 0. 2- Find the equation of motion (EOM) in terms of 0. 3- What is the natural frequency of the system? 0 L/2 8 Energy methods A Jo=m L²2 L/2 Joz-m R² R C B C 128

For the 3-DOF Industrial manipulator arm as shown in Figure 1,  determine the joint displacements using inverse kinematics approach for known position and orientation of the end of the arm point.   The link transformation matrices are given by

Please answer the questions provide f.b.d and differential equations , i just need these two things. Thanks in advance

6. The electro-mechanical system shown below consists of an electric motor with input voltage V which drives inertia I in the mechanical system (see torque T). Find the governing differential equations of motion for this electro-mechanical system in terms of the input voltage to the motor and output displacement y. Electrical System puthiy C V V₁ R bac (0) T bac T Motor - Motor Input Voltage - Motor Back EMF = Kbac ( - Motor Angular Velocity - Motor Output Torque = K₂ i Kbacs K₁ - Motor Constants Mechanical System M T Frictionless Support

Whats the first equation (circled) and how did we get it ?