Problem #5: Transfer Function: Mechanical System 3 2. Variables: Mass terms; mi, m2 Damping term; b1...
Mechanical vibration subject 3. a. Consider the system of Figure 3. If C1 = C2 = C3 = 0, develops the equation of motion and predict the mass and stiffness matrices. Note that setting k3 = 0 in your solution should result in the stiffness matrix given by [ky + kz -k2 kz b. constructs the characteristics equation from Question 3(a) for the case m1 = 9 kg, m2 = 1 kg, k1 = 24 N/m, k2 = 3 N/m,...
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...
4. Two masses mi and m2 are connected to three springs of negligible mass having spring constants k1, k2 and k3, respectively. x2=0 Il k, Let xi and x2 represent The motion of the equations: displacements of masses mi and m2 from their equilibrium positions . coupled system is represented by the system of second-order differential d2x dt2 d2x2 Using Laplace transform to solve the system when k1 1 and x1(0) = 0, xi (0)--1 , x2(0) = 0, x(0)-1....
3. Consider the spring - mass system shown below, consisting of two masses mi and m2 sus- pended from springs with spring constants ki and k2, respectively. Assume that there is no damping in the system. a) Show that the displacements ai and r2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above result to show that the spring-mass system satisfies the following fourth order differential equation and c) Find the general solution...
Problem 2: Transfer Functions of Mechanical Systems. (20 Points) A model sketch for a two-mass mechanical system subjected to fluctuations (t) at the wall is provided in figure 2. Spring k, is interconnected with both spring ka and damper Os at the nodal point. The independent displacement of mass m is denoted by 1, the independent displacement of mass m, is denoted by r2, and the independent displacement of the node is denoted by ra. Assume a linear force-displacement/velocity relationship...
w a. Obtain the transfer functions X1(s)/U(s) and X2(s)/U(s) of the mechanical system shown in the figure. b. Solve the transfer function to retrieve the information on the response function (as a function of time t) by assuming the m1 = m2 and ki = ki =k3 C. Plot the response function d. Show the impact of doubling the mass m2 = 2m1 on the response function - plot it to compare it with that described in case C
Problem 3: For the mechanical system shown below, perform the following tasks: 1) Develop second-order differential equations of motion for the position of the two hinged bars assuming small angles of motion and using angular rotation of bars 1 and 2 as the output variables, 2) write the equations of motion in state-space form, 3) state the output vector for force in spring k2. Note: Gravity acts downward with acceleration 'g O2 dz m2, L2 my L d3 www.jwwww B...
2. For the following 3-DOF spring-mass system: (a) Derive the equations of motion. (b) Assuming ki-k2-k3-k and mi-m2-m3-m, determine the natural frequencies and mode shapes. rt
02 Obtain the transfer function Y(s)yU(s) of the system shown in Figure. The vertical motion u at point P is the input. This system is a simplified version of an automobile or motorcycle suspension system. (In the figure mi and ki represent the wheel mass and tire stiffness, respectively.) Assume that the displacements x and y are measured from their respective equilibrium positions in the absence of the input u. Use Newton second law to derive the movement equations.
3. (15 points) Find the equations of motion for mi and m2 as shown in Figure 1.jo) is the input force of the system and xi is the output function of the system. Assume gravity is not a factor. of the system, find the transfer f (t) C3 m2 mi Figure 1 3. (15 points) Find the equations of motion for mi and m2 as shown in Figure 1.jo) is the input force of the system and xi is the...