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The system shown below is a model of a rocket payload (m2) being housed in a pro- tective cradle (m1). Find the natural frequencies and mode shapes associated with the system if m1=0.001 kg, m2=0.01 kg, and k1=2 kN/m and k2=1 kN/m. Solve the problem by hand, but you can use Matlab to check your answers. Will the cradle do a good job of protecting the satellite from vibration when y1 has a frequency near the first natural frequency of the system? Why or why not?
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The system shown below is a model of a rocket payload (m2) being housed in a pro- tective cradle ...
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 (-?
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...
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...
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...
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...
Q4. For the system shown in Figure 4 where m=10 kg, 100 kN/m, the governing equations has been derived as (1) Find the...
Q4. For the system shown in Figure 4 where m=10 kg, 100 kN/m, the governing equations has been derived as (1) Find the natural frequencies of the system; (2) Determine the associated mode shapes; and (3) Obtain the vibration response if the initial conditions are given as x,(0)-0,x,(0)-0.001 m, 2E 2m 1n Figure 4
Q4. For the system shown in Figure 4 where m=10 kg, 100 kN/m, the governing equations has been derived as (1) Find the natural frequencies of...
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...
with steps please 04. For the system shown in Figure 4 where m-10 kg, k-100 kN/m, the governing equations has been d...
with steps please
04. For the system shown in Figure 4 where m-10 kg, k-100 kN/m, the governing equations has been derived as (1) Find the natural frequencies of the system; (2) Determine the associated mode shapes; and (3) Obtain the vibration response if the initial conditions are given as x,(0)-0,x,(0)-0.001 m, 2kE TIITTTUITTU Figure 4
04. For the system shown in Figure 4 where m-10 kg, k-100 kN/m, the governing equations has been derived as (1) Find the natural...
MatLab work preferred, but please show/describe process. I) 3-DOF Pendulum System Using matrix algebra, analyze the...
MatLab work preferred, but please show/describe process.
I) 3-DOF Pendulum System Using matrix algebra, analyze the vibration of following 3-DOF pendulum system. Where, a is the distance from the pivot point to the spring, and L is the length of the pendulum string. Derive: the equations of motion, the system natural frequencies and system's mode shapes 01 02 K2 mi m2 m3 Data: mi 5 kg m2 = 5 kg m3 5 kg k1 100 N/m k2 100 N/m L...
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 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 (-?
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...
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...
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...
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...
Q4. For the system shown in Figure 4 where m=10 kg, 100 kN/m, the governing equations has been derived as (1) Find the natural frequencies of the system; (2) Determine the associated mode shapes; and (3) Obtain the vibration response if the initial conditions are given as x,(0)-0,x,(0)-0.001 m, 2E 2m 1n Figure 4
Q4. For the system shown in Figure 4 where m=10 kg, 100 kN/m, the governing equations has been derived as (1) Find the natural frequencies of...
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...
with steps please
04. For the system shown in Figure 4 where m-10 kg, k-100 kN/m, the governing equations has been derived as (1) Find the natural frequencies of the system; (2) Determine the associated mode shapes; and (3) Obtain the vibration response if the initial conditions are given as x,(0)-0,x,(0)-0.001 m, 2kE TIITTTUITTU Figure 4
04. For the system shown in Figure 4 where m-10 kg, k-100 kN/m, the governing equations has been derived as (1) Find the natural...
MatLab work preferred, but please show/describe process.
I) 3-DOF Pendulum System Using matrix algebra, analyze the vibration of following 3-DOF pendulum system. Where, a is the distance from the pivot point to the spring, and L is the length of the pendulum string. Derive: the equations of motion, the system natural frequencies and system's mode shapes 01 02 K2 mi m2 m3 Data: mi 5 kg m2 = 5 kg m3 5 kg k1 100 N/m k2 100 N/m L...
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,...
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