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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 systern shown in Figure 4 where m=10 kg, k = 100 kN/m, the governing equations has been derived as (1) Find...
Q4. For the systern 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 2k E 2m Figure 4
Q4. For the systern shown in Figure 4 where m=10 kg, k = 100 kN/m, the governing equations has...
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...
Problem 4 (20%) Figure 5 shows a uniform elastic bar fixed at one end and attached to a mass M at the other end. The cr...
Problem 4 (20%) Figure 5 shows a uniform elastic bar fixed at one end and attached to a mass M at the other end. The cross sectional area for the bar is A, mass density per unit length p, modulus of elasticity E and second moment of area I. For the longitudinal vibration: S Set the necessary coordinate system, governing equation of motion and boundary conditions a. b. Derive the general solution. Explain how you can obtain the natural frequencies...
4.11 Compute the natural frequencies and mode shapes of the following system: 4 0 4 X10...
4.11 Compute the natural frequencies and mode shapes of the following system: 4 0 4 X10 -2 X= 0 1 1 -2 and Calculate the response of the system to the initial conditions: x, 1 2 -2120 20
4.11 Compute the natural frequencies and mode shapes of the following system: 4 0 4 X10 -2 X= 0 1 1 -2 and Calculate the response of the system to the initial conditions: x, 1 2 -2120 20
(t) 8k mm sm For the vibratory system shown in the figure, k=15000 N/m and m=1.5...
(t) 8k mm sm For the vibratory system shown in the figure, k=15000 N/m and m=1.5 kg. a. Derive the equations of motion. b. Calculate the natural frequencies. c. Find the ratio of the mode amplitudes and draw the mode shapes. Xy(t) w 3k 2m TA X2(t)
Problem: Find the natural frequencies of the system shown in Figure. Take m 2 kg ma 2.5 kg ms 3.0...
Problem: Find the natural frequencies of the system shown in Figure. Take m 2 kg ma 2.5 kg ms 3.0 kg me = 1.5 kg 914 Given: Four degree of freedom spring-mass system with given masses an stiffnesses. Find: Natural frequencies and mode shapes. Approach: Find the eigenvalues and eigenvectors of the dynamical matrix. 1. Determine [m] and [k] matrices of the vibrating system with all details 2. Determine [DI matrix. 3. Determine Natural frequencies and mode shapes analytically 3....
Q3. For the system in Figure 3 where 0 and angles, and are the rotary inertias of the two disks with are the rotati...
Q3. For the system in Figure 3 where 0 and angles, and are the rotary inertias of the two disks with are the rotational radius r and 2r, respectively, 2r (1) Find its total kinetic energy, total potential energy and Lagrangian in terms of 0, and 0 (2) Derive the equations of motion using Lagrangian equation method (3) Put the equations of motion in matrix form, and (4) Calculate the natural frequencies and the associated mode Fosin shapes if m...
The system shown below is a model of a rocket payload (m2) being housed in a pro- tective cradle ...
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...
Q3. For the system in Figure 3 where and θ2 are the rotational angles, and are the rotary inertias of the two disks with radius r and 2r, respectively, 2r (1) Find its total kinetic energy, total pot...
Q3. For the system in Figure 3 where and θ2 are the rotational angles, and are the rotary inertias of the two disks with radius r and 2r, respectively, 2r (1) Find its total kinetic energy, total potential energy and Lagrangian in terms of, and (2) Derive the equations of motion using Lagrangian equation method, (3) Put the equations of motion in matrix form, and (4) Calculate the natural frequencies and the associated mode shapes if m-30 g, 4-8 x...
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 (-?
Q4. For the systern 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 2k E 2m Figure 4
Q4. For the systern shown in Figure 4 where m=10 kg, k = 100 kN/m, the governing equations has...
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...
Problem 4 (20%) Figure 5 shows a uniform elastic bar fixed at one end and attached to a mass M at the other end. The cross sectional area for the bar is A, mass density per unit length p, modulus of elasticity E and second moment of area I. For the longitudinal vibration: S Set the necessary coordinate system, governing equation of motion and boundary conditions a. b. Derive the general solution. Explain how you can obtain the natural frequencies...
4.11 Compute the natural frequencies and mode shapes of the following system: 4 0 4 X10 -2 X= 0 1 1 -2 and Calculate the response of the system to the initial conditions: x, 1 2 -2120 20
4.11 Compute the natural frequencies and mode shapes of the following system: 4 0 4 X10 -2 X= 0 1 1 -2 and Calculate the response of the system to the initial conditions: x, 1 2 -2120 20
(t) 8k mm sm For the vibratory system shown in the figure, k=15000 N/m and m=1.5 kg. a. Derive the equations of motion. b. Calculate the natural frequencies. c. Find the ratio of the mode amplitudes and draw the mode shapes. Xy(t) w 3k 2m TA X2(t)
Problem: Find the natural frequencies of the system shown in Figure. Take m 2 kg ma 2.5 kg ms 3.0 kg me = 1.5 kg 914 Given: Four degree of freedom spring-mass system with given masses an stiffnesses. Find: Natural frequencies and mode shapes. Approach: Find the eigenvalues and eigenvectors of the dynamical matrix. 1. Determine [m] and [k] matrices of the vibrating system with all details 2. Determine [DI matrix. 3. Determine Natural frequencies and mode shapes analytically 3....
Q3. For the system in Figure 3 where 0 and angles, and are the rotary inertias of the two disks with are the rotational radius r and 2r, respectively, 2r (1) Find its total kinetic energy, total potential energy and Lagrangian in terms of 0, and 0 (2) Derive the equations of motion using Lagrangian equation method (3) Put the equations of motion in matrix form, and (4) Calculate the natural frequencies and the associated mode Fosin shapes if m...
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...
Q3. For the system in Figure 3 where and θ2 are the rotational angles, and are the rotary inertias of the two disks with radius r and 2r, respectively, 2r (1) Find its total kinetic energy, total potential energy and Lagrangian in terms of, and (2) Derive the equations of motion using Lagrangian equation method, (3) Put the equations of motion in matrix form, and (4) Calculate the natural frequencies and the associated mode shapes if m-30 g, 4-8 x...
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 (-?
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