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2. For the following 3-DOF spring-mass system: (a) Derive the equations of motion. (b) Assuming ki-k2-k3-k...
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...
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 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...
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...
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...
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
Problem 2) For a 2 DOF system the equations of motion are given as: m9 [m...
Problem 2) For a 2 DOF system the equations of motion are given as: m9 [m OX -M29 2 m29 0 mal -29 Where m=m2 Em g -gravity and L =length a) Determine the frequencies and mode shapes. b) Verify that the natural modes are orthogonal. c) Determine the response (0) (0)) Note: xi(t) = XO, xa(t) = 0 and 1) = xo.* () = 0 d) If the system is excited by a harmonic force F. (t) =F, sinot,...
1. Derive the equations of motion of the system shown in Fig 1 by using Lagrange's...
1. Derive the equations of motion of the system shown in Fig 1 by using Lagrange's equations. Find the natural frequencies and mode shapes of the dynamical system for k 1 N/m, k-2 N/m, k I N/m, and mi 2 kg, m l kg, m -2 kg. scale the eigenvectors matrix Ф in order to achieve a mass normalized eigenvectors matrix Φ such that: F40 Fan Fig. 1
3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a...
3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a system (ki, mi) subject to a harmonic force F(t) = Fo cosot. (a) Derive the amplitudes of steady-state response for mi and m2. (b) Find the relation between k2 and m2 that leads to no steady state vibration of m.
3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a system (ki, mi) subject to a harmonic force...
3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a...
3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a system (ki, m) subject to a harmonic force F(t) Fo cos @t. (a) Derive the amplitudes of steady-state response for mi and m2. (b) Find the relation between k2 and m2 that leads to no steady state vibration of mi.
3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a system (ki, m) subject to a harmonic force...
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...
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 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...
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...
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...
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
Problem 2) For a 2 DOF system the equations of motion are given as: m9 [m OX -M29 2 m29 0 mal -29 Where m=m2 Em g -gravity and L =length a) Determine the frequencies and mode shapes. b) Verify that the natural modes are orthogonal. c) Determine the response (0) (0)) Note: xi(t) = XO, xa(t) = 0 and 1) = xo.* () = 0 d) If the system is excited by a harmonic force F. (t) =F, sinot,...
1. Derive the equations of motion of the system shown in Fig 1 by using Lagrange's equations. Find the natural frequencies and mode shapes of the dynamical system for k 1 N/m, k-2 N/m, k I N/m, and mi 2 kg, m l kg, m -2 kg. scale the eigenvectors matrix Ф in order to achieve a mass normalized eigenvectors matrix Φ such that: F40 Fan Fig. 1
3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a system (ki, mi) subject to a harmonic force F(t) = Fo cosot. (a) Derive the amplitudes of steady-state response for mi and m2. (b) Find the relation between k2 and m2 that leads to no steady state vibration of m.
3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a system (ki, mi) subject to a harmonic force...
3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a system (ki, m) subject to a harmonic force F(t) Fo cos @t. (a) Derive the amplitudes of steady-state response for mi and m2. (b) Find the relation between k2 and m2 that leads to no steady state vibration of mi.
3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a system (ki, m) subject to a harmonic force...
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