![2. (40 points) Keep 3 digits after decimal points A toy vehicle suspension system is given as following. k1-10 N/m, k2- 50 N/m, mi 2 kg, m2 1 kg. Calculate a) Natural frequencies (10 points) b) Vectors ui and u2 (15 points) c) Given the initial condition x(0) [1, 0] and v(0) Car mas:s Car spring [1,0]T, calculate the free response of the system (15 points). k2 Tire stiffness Tire mass](http://img.homeworklib.com/questions/daf3c430-b313-11eb-a5d4-17698b0d7a4a.png?x-oss-process=image/resize,w_560)
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2. (40 points) Keep 3 digits after decimal points A toy vehicle suspension system is given...
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...
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 (-?
1 1 2 m2 1. Consider the system above. Derive the equation of motion and calculate the mass and s...
Please provide any MATLAB code you used for plotting.
1 1 2 m2 1. Consider the system above. Derive the equation of motion and calculate the mass and stiffness matrices. a) Calculate the characteristic equation forthe case m 9 kg m 1 kg k 24 N/m k2 3 N/mk3- 3 N/m and solve for the system's natural frequencies. b.) Calculate the eigenvectors u1 and u2 c.) Calculate xi(t) and x2(t), given x2(0)-1 mm, and xi(0) - vz(0) -vi(0) 0 d.)...
M1 m2 Figure 1: 2dof 1. Consider the system above. Derive the equation of motion and calculate th...
m1 m2 Figure 1: 2dof 1. Consider the system above. Derive the equation of motion and calculate the mass and stiffness matrices Note that setting k30 in your solution should result in the stiffness matrix given by Eq. (4.9). a. Calculate the characteristic equation from problem 4.1 for the case m1-9 kg m2-1 kg ki-24 N/m 2 3 N/m k 3 N/m and solve for the system's natural frequencies. b. Calculate the eigenvectors u1 and u2. c. Calculate 띠(t) and...
1) (35 points) A model of a vehicle suspension system is shown below. The of a...
1) (35 points) A model of a vehicle suspension system is shown below. The of a 500 kg vehicle is connected to the wheels through a suspension system that is modeled as a spring in parallel with a viscous damper. The wheels are assumed to be rigid and follow the road contour which is also shown below. If the vehicle travels at a constant speed of 52 m/s, what is the acceleration amplitude of the vehicle? E m500 kg k=...
1) (35 points) A model of a vehicle suspension system is shown below. The of a...
1) (35 points) A model of a vehicle suspension system is shown below. The of a 500 kg vehicle is connected to the wheels through a suspension system that is modeled as a spring in parallel with a viscous damper. The wheels are assumed to be rigid and follow the road contour which is also shown below. If the vehicle travels at a constant speed of 52 m/s, what is the acceleration amplitude of the vehicle? m = 500 kg...
(40pts) The suspension system for one wheel of a pickup truck is illustrated in the following...
(40pts) The suspension system for one wheel of a pickup truck is illustrated in the following figure. The mass of the vehicle distributed on this wheel is mi and the mass of the wheel is m2. The suspension spring has a spring constant kı and the tire has a spring constant of k2. The damping constant of the shock absorber is b. Assume the truck's vertical displacement yi(t) is the output and the road surface profile x(t) is the input....
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...
Additional Prob. 1: Consider a two-mass quarter-car model of a suspension system as shown in figure....
Additional Prob. 1: Consider a two-mass quarter-car model of a suspension system as shown in figure. The system properties are: m1 = 240 kg, m2 = 36 kg, k1 = 1.6 x 104 N/m, k2 = 1.6 x 105 N/m, C1 = 98 N-s/m a. Find equations of motion for the system. c. If y(t) is a unit step function, find the responses X1 and x between 0-10 s using Simulink. m m,
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...
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 (-?
Please provide any MATLAB code you used for plotting.
1 1 2 m2 1. Consider the system above. Derive the equation of motion and calculate the mass and stiffness matrices. a) Calculate the characteristic equation forthe case m 9 kg m 1 kg k 24 N/m k2 3 N/mk3- 3 N/m and solve for the system's natural frequencies. b.) Calculate the eigenvectors u1 and u2 c.) Calculate xi(t) and x2(t), given x2(0)-1 mm, and xi(0) - vz(0) -vi(0) 0 d.)...
m1 m2 Figure 1: 2dof 1. Consider the system above. Derive the equation of motion and calculate the mass and stiffness matrices Note that setting k30 in your solution should result in the stiffness matrix given by Eq. (4.9). a. Calculate the characteristic equation from problem 4.1 for the case m1-9 kg m2-1 kg ki-24 N/m 2 3 N/m k 3 N/m and solve for the system's natural frequencies. b. Calculate the eigenvectors u1 and u2. c. Calculate 띠(t) and...
1) (35 points) A model of a vehicle suspension system is shown below. The of a 500 kg vehicle is connected to the wheels through a suspension system that is modeled as a spring in parallel with a viscous damper. The wheels are assumed to be rigid and follow the road contour which is also shown below. If the vehicle travels at a constant speed of 52 m/s, what is the acceleration amplitude of the vehicle? E m500 kg k=...
1) (35 points) A model of a vehicle suspension system is shown below. The of a 500 kg vehicle is connected to the wheels through a suspension system that is modeled as a spring in parallel with a viscous damper. The wheels are assumed to be rigid and follow the road contour which is also shown below. If the vehicle travels at a constant speed of 52 m/s, what is the acceleration amplitude of the vehicle? m = 500 kg...
(40pts) The suspension system for one wheel of a pickup truck is illustrated in the following figure. The mass of the vehicle distributed on this wheel is mi and the mass of the wheel is m2. The suspension spring has a spring constant kı and the tire has a spring constant of k2. The damping constant of the shock absorber is b. Assume the truck's vertical displacement yi(t) is the output and the road surface profile x(t) is the input....
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...
Additional Prob. 1: Consider a two-mass quarter-car model of a suspension system as shown in figure. The system properties are: m1 = 240 kg, m2 = 36 kg, k1 = 1.6 x 104 N/m, k2 = 1.6 x 105 N/m, C1 = 98 N-s/m a. Find equations of motion for the system. c. If y(t) is a unit step function, find the responses X1 and x between 0-10 s using Simulink. m m,
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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