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1. A two story building is represented in the figure below by a lumped mass systen...
For a mass-spring system shown in the figure below. Write the dynamic equations in matrix form...
For a mass-spring system shown in the figure below. Write the dynamic equations in matrix form and find the natural frequencies for this system, eigen values, eigen vectors and mode shapes assuming: m1=1 kg, m2=4 kg, k1=k3=10 N/m, and k2=2 N/m. / ر2 دی) x1(0) x2(0) K3 K1 W K2 mi W4 m2 (-?
2: An automobile is traveling on a rough road (1) Draw the free-body diagrams of the...
2: An automobile is traveling on a rough road (1) Draw the free-body diagrams of the two masses and set up the equations of motion using the vertical displacements of the two masses. Note that the base excitation function y(t) is also in the vertical direction. Put the equations in matrix form Identify the mass matrix and stiffness matrix (2) Solve the structural eigenvalue problem to find the natural frequencies and mode kN shapes considering such data: m1 1000 kg,...
For the system shown in Figure 6, a. How many degrees of freedom is this system and why? b. Write the equations of moti...
For the system shown in Figure 6, a. How many degrees of freedom is this system and why? b. Write the equations of motion. For the remainder parts, assume alll the dampers are removed: c. If Ki=K3 and mim3, set the necessary matrix to find the natural frequencies and mode shapes d. For part c above, determine and explain how to get the natural frequencies. m1 Ty Absorber тз k1 С1 k3 m2 C2
For the system shown in Figure...
Problem 5 (20%) For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3 0...
Problem 5 (20%) For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3 0 (the upper end is fixed and K1 and K2=K Write the equations of motion. Set the necessary matrix to find the natural frequencies and mode shapes (5) (5) (5) 1. 2. 3. Determine and explain how to get the natural frequencies. m2 Figure 5 www
Problem 5 (20%) For the system shown in Figure...
Figure 5 shows a pick-up truck of a total mass mi transporting a small cart of a mass m2. The sma...
Figure 5 shows a pick-up truck of a total mass mi transporting a small cart of a mass m2. The small cart is hitched through two springs of axial stiffness k each to the truck (b) body. Absolute displacement of the truck is xi while that of the cart is x2 (i) Find the relative motion (n-m) of the cart when the truck is subjected to a (7 marks) Find the natural frequencies and mode shapes of this two-degree-of-freedom harmonic...
For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3-0 (the upper end...
For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3-0 (the upper end is fixed and K1 and K2=K (5) Write the equations of motion. Set the necessary matrix to find the natural frequencies and mode shapes Determine and explain how to get the natural frequencies 1. (5) (5) 2. 3. Figure 5 ww ww-
For the system shown in Figure 5, a. How many degrees of freedom...
Please answer question number 4, the answer to question 3 is unnecessary. 3. A two-story building...
Please answer question number 4, the answer to question 3 is
unnecessary.
3. A two-story building is represented in Fig. 3 by a lamped mass system in which mi=1/2m2 and ki = ½ k2. Use Lagrange's equations to derive the differential equations governing the motion of the building and find its normal modes (characteristic frequencies and mode shapes).-r ,m/ Fig. 3 4. In Problem 3 determine the equation of motion of each mass by the normal mode summation method in...
4. Two masses mi and m2 are connected to three springs of negligible mass having spring constants...
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....
EXERCISE 2 The following system is composed by two bodies of mass m, and m2 and five identical strings of stiffness k....
EXERCISE 2 The following system is composed by two bodies of mass m, and m2 and five identical strings of stiffness k. Friction and any other dissipative terms are negligible. k Draw the free body diagrams for the two bodies. a) | y1 |F b) Write the equation of motion in matrix form, expressing the content of each matrix/vector m1 c) Calculate the natural frequencies of the system, knowing that m1 1 kg, m2 2 kg and k = 1000...
Problem 2) For a 2 DOF system the equations of motion are given as: [mi 0...
Problem 2) For a 2 DOF system the equations of motion are given as: [mi 0 0 m2 (X2 mig L -m29 L -m29 L m29 L Where m1 =m2 =m g=gravity and L =length a) Determine the frequencies and mode shapes. b) Verify that the natural modes are orthogonal. c) Determine the response fX:(0) Note: x1(t) = xo , x2(t) = 0 and xi(t) = xo , iz(t) = 0 d) If the system is excited by a harmonic...
For a mass-spring system shown in the figure below. Write the dynamic equations in matrix form and find the natural frequencies for this system, eigen values, eigen vectors and mode shapes assuming: m1=1 kg, m2=4 kg, k1=k3=10 N/m, and k2=2 N/m. / ر2 دی) x1(0) x2(0) K3 K1 W K2 mi W4 m2 (-?
2: An automobile is traveling on a rough road (1) Draw the free-body diagrams of the two masses and set up the equations of motion using the vertical displacements of the two masses. Note that the base excitation function y(t) is also in the vertical direction. Put the equations in matrix form Identify the mass matrix and stiffness matrix (2) Solve the structural eigenvalue problem to find the natural frequencies and mode kN shapes considering such data: m1 1000 kg,...
For the system shown in Figure 6, a. How many degrees of freedom is this system and why? b. Write the equations of motion. For the remainder parts, assume alll the dampers are removed: c. If Ki=K3 and mim3, set the necessary matrix to find the natural frequencies and mode shapes d. For part c above, determine and explain how to get the natural frequencies. m1 Ty Absorber тз k1 С1 k3 m2 C2
For the system shown in Figure...
Problem 5 (20%) For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3 0 (the upper end is fixed and K1 and K2=K Write the equations of motion. Set the necessary matrix to find the natural frequencies and mode shapes (5) (5) (5) 1. 2. 3. Determine and explain how to get the natural frequencies. m2 Figure 5 www
Problem 5 (20%) For the system shown in Figure...
Figure 5 shows a pick-up truck of a total mass mi transporting a small cart of a mass m2. The small cart is hitched through two springs of axial stiffness k each to the truck (b) body. Absolute displacement of the truck is xi while that of the cart is x2 (i) Find the relative motion (n-m) of the cart when the truck is subjected to a (7 marks) Find the natural frequencies and mode shapes of this two-degree-of-freedom harmonic...
For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3-0 (the upper end is fixed and K1 and K2=K (5) Write the equations of motion. Set the necessary matrix to find the natural frequencies and mode shapes Determine and explain how to get the natural frequencies 1. (5) (5) 2. 3. Figure 5 ww ww-
For the system shown in Figure 5, a. How many degrees of freedom...
Please answer question number 4, the answer to question 3 is
unnecessary.
3. A two-story building is represented in Fig. 3 by a lamped mass system in which mi=1/2m2 and ki = ½ k2. Use Lagrange's equations to derive the differential equations governing the motion of the building and find its normal modes (characteristic frequencies and mode shapes).-r ,m/ Fig. 3 4. In Problem 3 determine the equation of motion of each mass by the normal mode summation method in...
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....
EXERCISE 2 The following system is composed by two bodies of mass m, and m2 and five identical strings of stiffness k. Friction and any other dissipative terms are negligible. k Draw the free body diagrams for the two bodies. a) | y1 |F b) Write the equation of motion in matrix form, expressing the content of each matrix/vector m1 c) Calculate the natural frequencies of the system, knowing that m1 1 kg, m2 2 kg and k = 1000...
Problem 2) For a 2 DOF system the equations of motion are given as: [mi 0 0 m2 (X2 mig L -m29 L -m29 L m29 L Where m1 =m2 =m g=gravity and L =length a) Determine the frequencies and mode shapes. b) Verify that the natural modes are orthogonal. c) Determine the response fX:(0) Note: x1(t) = xo , x2(t) = 0 and xi(t) = xo , iz(t) = 0 d) If the system is excited by a harmonic...
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