Problem 7: Consider the two-degrees of freedom system shown in the figure below, where each disk...
PROBLEM 1 (35 %) The mechanical system in the figure below consists of a disk of radius r, a block of mass m, a spring of stiffness (spring constant) k, and a damper with damping ratio b. The disk has moment of inertia Jabout its center of mass (pivot point O), and the block is subjected to an external force t) as shown in the figure. The spring is unstressed when x 0= 0. Assume small 0. (a) (10 points)...
1. Given the spring-mass-damper system in the figure below T3 T1 T2 b2 b1 k3 (a) Find the equations of motion for each of the masses 脳. Fi(s) (b) Assume F1 0 and find the transfer function (c) Assume Fs 0 and find the transfer function (d) Write the equations in matrix-vector form: M.ї + Bi + Kx-F where z is a 3 x 1 vector with the displacements r,2, r3 as components, M is the mass matrix, B is...
Problem3 The following problem is intended to be solved by hand. For the structure shown below A.) Label the structure degrees of freedom (free only) and number the elements B.) For each element, determine the stiffness matrix in global element coordinates. Label each row and column of each element matrix with its corresponding global DoF. C.) Assemble the structure stiffness matrix Kfr from the element global stiffness matrices D.) Calculate the deflection of the free DoFs. 5 ft 500 k...
For the problem: A) how many degrees of freedom does the system have? B) sketch a free-body diagram for each rigid body in the system. C) Write Newton’s second law of moments for each rigid body. D) List the unknowns, and compare to the number of equations. If necessary specify any kinematic constraints that are required to provide enough equations to determine the unknowns. 2.24 A mechanical system containing translating and rotating components is shown below. The left end of...
Consider the system shown in the figure below. The mass moment of inertia of the bar about the point O is JO, and the torsional stiffness of the spring attached to the pivot point is kt . Assume that there is gravity loading. The centre of gravity of the bar is midways, as shown in the figure. Question 2 Consider the system shown in the figure below. The mass moment of inertia of the bar about the point O is...
2. Consider the system shown in the figure below, comprised of the same motor, steel beam, steel cable and crate All assumptions and properties are the same with one exception; the cable is no longer considered as rigid Cable properties: length = 4 m, diameter = 0.007 m, E = 207 GPa, Calculate the equivalent stiffness of the cable, in units of N/m. (See table 4.1.1 in your textbook) Draw an equivalent system diagram where the beam and cable each...
Consider the system shown in the figure right, where two blocks m1=5 kg, and m2=10 kg are connected to each other by a string that passes through a massless pulley. The stiffness constant of the spring attached to m1 and the wall is k=120N/m and the coefficient of kinetic friction between m1 and the surface is given to be μk=0.2. If the system is released from rest when the spring is at its equilibrium length and m2 is at a...