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B-9-15 Hint: Transform into modal coordinates to find the solution in modal coordinates then transform the...
Homework 8: Modal and Direct Solution Approaches Figure 1 shows a system with two masses. The two...
Homework 8: Modal and Direct Solution Approaches Figure 1 shows a system with two masses. The two coordinates of which the origins are set up at the unstretched spring positions are also shown in Fig. 1. The system is excited by the force f(t) 1. (a) Draw the FBDs for the system and show that the EOMs can be written as (b) Find the undamped, natural frequencies and the corresponding mode shapes of the system for the given system parameters...
MEMB343 MECHANICAL VIBRATIONS ASSIGNMENT l. For the system shown in Figure 1, where mi=5 kg, m,-10 kg, ki=1000 N/m, k2-500 N/m, k, 2000 N/m, fi-100sin(15t) N and f-0, use modal analysis to determine...
MEMB343 MECHANICAL VIBRATIONS ASSIGNMENT l. For the system shown in Figure 1, where mi=5 kg, m,-10 kg, ki=1000 N/m, k2-500 N/m, k, 2000 N/m, fi-100sin(15t) N and f-0, use modal analysis to determine the amplitudes of masses m, and m2. The equations of motion are given as sin(15t), wth natura frequencies 5 01[i, 0 10 500-500x, 500 2500jx, x,[100 ω,-14.14 rad's and a, = 18.71 rad/s, and mode shapes, Φ',, and Φ' k, Im Figure 1
MEMB343 MECHANICAL VIBRATIONS ASSIGNMENT...
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,...
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...
Question 6 Ci m, I k2 Figure Q6 A unform bar of mass m and length...
Question 6 Ci m, I k2 Figure Q6 A unform bar of mass m and length is pivoted at C as indicated in Figure Q6 The bar carries a mass M at D and is supported by springs kt, k2 and dampers c1, r3 as shown Let , 12, 13 be the displacements at the positions shown when the system is given a small angular displacement θ from the equilibrium horizontal position Given that C and D are distances 4...
Please answer the questions for Part 1 and Part 2 showing all steps, using the provided...
Please answer the questions for Part 1 and Part 2 showing all
steps, using the provided data values.
Many thanks.
M2 2 C2 2' 2 2 C2 2'2 Spring steel Mi k1 C1 2'2 1 C1 Base y(t) Base movement Figure 2 shows a shear building with base motion. This building is modelled as a 2 DOF dynamic system where the variables of ml-3.95 kg, m2- 0.65 kg, kl-1200 N/m, k2- 68 N/m, cl- 0.40 Ns/m, c2- 0.70Ns/m The base...
9. (a) Find the inverse Fourier transform of the following function 1 (2 iw)(5 iw) (b)...
9. (a) Find the inverse Fourier transform of the following function 1 (2 iw)(5 iw) (b) The displacement of a particular mechanical system is governed by the following ordinary differential equation dy 10y f(t) 7 dt where y(t) is the displacement and f(t) is the applied load Page 2 of 4 MATH2124 SaMplE EXAM IV i Use the Fourier transform to obtain the impulse response h(t) of the mechanical system (ii) If the applied load is f(t) = H (t1)-...
Mi k2 b yi m2 Figure 5-45 Mechanical system. Assuming that mi 10 kg, m2 5 kg, b 10 N-s/m, k 40 N/...
mi k2 b yi m2 Figure 5-45 Mechanical system. Assuming that mi 10 kg, m2 5 kg, b 10 N-s/m, k 40 N/m, and k 20 N/m and that input force u is a constant force of 5 N, obtain the response of the sys- tem. Plot the response curves n(t) versus r and y2(t) versus t with MATLAB Problem B-5-23 Consider the system shown in Figure 5-45. The system is at rest for t < 0. The dis placements...
For the mechanical system shown below find the input-output equation relating xolt) to the displacement input...
For the mechanical system shown below find the input-output equation relating xolt) to the displacement input x(t) 1. ド ド Ki Derive the transfer function X,G)/X, (s)of the mechanical system shown below. The displacements x, and xo are measured from their respective equilibrium potions. Is the system a first-order system if so, what is the time constant? 2. k1 bz k2 3. Consider the mechanical system shown below. The system is initially at rest. The displacements x, and x2 are...
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...
Homework 8: Modal and Direct Solution Approaches Figure 1 shows a system with two masses. The two coordinates of which the origins are set up at the unstretched spring positions are also shown in Fig. 1. The system is excited by the force f(t) 1. (a) Draw the FBDs for the system and show that the EOMs can be written as (b) Find the undamped, natural frequencies and the corresponding mode shapes of the system for the given system parameters...
MEMB343 MECHANICAL VIBRATIONS ASSIGNMENT l. For the system shown in Figure 1, where mi=5 kg, m,-10 kg, ki=1000 N/m, k2-500 N/m, k, 2000 N/m, fi-100sin(15t) N and f-0, use modal analysis to determine the amplitudes of masses m, and m2. The equations of motion are given as sin(15t), wth natura frequencies 5 01[i, 0 10 500-500x, 500 2500jx, x,[100 ω,-14.14 rad's and a, = 18.71 rad/s, and mode shapes, Φ',, and Φ' k, Im Figure 1
MEMB343 MECHANICAL VIBRATIONS ASSIGNMENT...
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,...
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...
Question 6 Ci m, I k2 Figure Q6 A unform bar of mass m and length is pivoted at C as indicated in Figure Q6 The bar carries a mass M at D and is supported by springs kt, k2 and dampers c1, r3 as shown Let , 12, 13 be the displacements at the positions shown when the system is given a small angular displacement θ from the equilibrium horizontal position Given that C and D are distances 4...
Please answer the questions for Part 1 and Part 2 showing all
steps, using the provided data values.
Many thanks.
M2 2 C2 2' 2 2 C2 2'2 Spring steel Mi k1 C1 2'2 1 C1 Base y(t) Base movement Figure 2 shows a shear building with base motion. This building is modelled as a 2 DOF dynamic system where the variables of ml-3.95 kg, m2- 0.65 kg, kl-1200 N/m, k2- 68 N/m, cl- 0.40 Ns/m, c2- 0.70Ns/m The base...
9. (a) Find the inverse Fourier transform of the following function 1 (2 iw)(5 iw) (b) The displacement of a particular mechanical system is governed by the following ordinary differential equation dy 10y f(t) 7 dt where y(t) is the displacement and f(t) is the applied load Page 2 of 4 MATH2124 SaMplE EXAM IV i Use the Fourier transform to obtain the impulse response h(t) of the mechanical system (ii) If the applied load is f(t) = H (t1)-...
mi k2 b yi m2 Figure 5-45 Mechanical system. Assuming that mi 10 kg, m2 5 kg, b 10 N-s/m, k 40 N/m, and k 20 N/m and that input force u is a constant force of 5 N, obtain the response of the sys- tem. Plot the response curves n(t) versus r and y2(t) versus t with MATLAB Problem B-5-23 Consider the system shown in Figure 5-45. The system is at rest for t < 0. The dis placements...
For the mechanical system shown below find the input-output equation relating xolt) to the displacement input x(t) 1. ド ド Ki Derive the transfer function X,G)/X, (s)of the mechanical system shown below. The displacements x, and xo are measured from their respective equilibrium potions. Is the system a first-order system if so, what is the time constant? 2. k1 bz k2 3. Consider the mechanical system shown below. The system is initially at rest. The displacements x, and x2 are...
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...
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