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For the system shown in Figure 6, a. How many degrees of freedom is this system and why? b. Write the equations of moti...
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...
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...
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. For the following 3-DOF spring-mass system: (a) Derive the equations of motion. (b) Assuming ki-k2-k3-k...
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
Mechanical vibration subject 3. a. Consider the system of Figure 3. If C1 = C2 =...
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,...
For the system below (a) Write equation of motions in matrix form (b) compute for the...
For the system below (a) Write equation of motions in matrix form (b) compute for the eigenvalues natural frequencies square) and (c) compute eigenvectors (mode shapes) vectors as j-1 (d) Sketch mode shapes r k3 k, k2 C2 m2 F. 2 Assume
MatLab analysis preferred, but please show the process. II) 3-DOF Torsional System Using matrix algebra, analyze...
MatLab analysis preferred, but please show the process.
II) 3-DOF Torsional System Using matrix algebra, analyze the natural frequencies of the following 3-DOF shaft system. First setup the equations of motion, express the system in matrix form, and then use MATLAB to calculate the natural frequencies and the mode shapes. K2 K3 K4 J1 J2 J3 Data: J: = 500 lb.in.s- J2 750 lb.in.s2 J3 1000 lb.in.s? K1-2x106 lb.in/rad K2 106 Ib.in/rad K3 106 Ib.in/rad K4 2x106 lb.in/rad
1. A two story building is represented in the figure below by a lumped mass systen...
1. A two story building is represented in the figure below by a lumped mass systen in which m1 = m2 and k1 = k2. The ground is given a harmonic motion y Ysin at. Draw the appropriate free body diagrams. (5 points) a. b. Write the equations of motion in matrix form. (5 points) c. Solve for the natural frequencies and mode shapes. (10 points) d. Solve for the displacement amplitude response of xi and x2. (10 points)
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are...
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are at the SEPs is shown in Figure 1. The mass of m2 is acted by the external force of f(t). Assume that the cable between the two springs, k2 and k3 is not stretchable. Solve the following problems (a) Draw free-body diagrams for the two masses and derive their EOMs (b) Represent the EOMs in a matrix fornm (c) Find the undamped, natural frequencies...
Test Consider a two-degrees-of-freedom system shown below. ド. PN What is the amplitude of vibration (particular solution only) of mass 2 (at the input frequency)? The answer must be positive. Ke...
Test Consider a two-degrees-of-freedom system shown below. ド. PN What is the amplitude of vibration (particular solution only) of mass 2 (at the input frequency)? The answer must be positive. Keep 3 significant figures, and omit units. Use m1 2 kg m2 4 kg k1 147 N/m k2 146 N/m K3 192 N/m F1 # 411 cos(0.50 N Note that the system is not damped. The homogeneous response does not decay to zero. The masses vibrates at three different frequencies...
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...
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...
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. 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
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,...
For the system below (a) Write equation of motions in matrix form (b) compute for the eigenvalues natural frequencies square) and (c) compute eigenvectors (mode shapes) vectors as j-1 (d) Sketch mode shapes r k3 k, k2 C2 m2 F. 2 Assume
MatLab analysis preferred, but please show the process.
II) 3-DOF Torsional System Using matrix algebra, analyze the natural frequencies of the following 3-DOF shaft system. First setup the equations of motion, express the system in matrix form, and then use MATLAB to calculate the natural frequencies and the mode shapes. K2 K3 K4 J1 J2 J3 Data: J: = 500 lb.in.s- J2 750 lb.in.s2 J3 1000 lb.in.s? K1-2x106 lb.in/rad K2 106 Ib.in/rad K3 106 Ib.in/rad K4 2x106 lb.in/rad
1. A two story building is represented in the figure below by a lumped mass systen in which m1 = m2 and k1 = k2. The ground is given a harmonic motion y Ysin at. Draw the appropriate free body diagrams. (5 points) a. b. Write the equations of motion in matrix form. (5 points) c. Solve for the natural frequencies and mode shapes. (10 points) d. Solve for the displacement amplitude response of xi and x2. (10 points)
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are at the SEPs is shown in Figure 1. The mass of m2 is acted by the external force of f(t). Assume that the cable between the two springs, k2 and k3 is not stretchable. Solve the following problems (a) Draw free-body diagrams for the two masses and derive their EOMs (b) Represent the EOMs in a matrix fornm (c) Find the undamped, natural frequencies...
Test Consider a two-degrees-of-freedom system shown below. ド. PN What is the amplitude of vibration (particular solution only) of mass 2 (at the input frequency)? The answer must be positive. Keep 3 significant figures, and omit units. Use m1 2 kg m2 4 kg k1 147 N/m k2 146 N/m K3 192 N/m F1 # 411 cos(0.50 N Note that the system is not damped. The homogeneous response does not decay to zero. The masses vibrates at three different frequencies...
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