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2: An automobile is traveling on a rough road (1) Draw the free-body diagrams of the...
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...
Figure 1 shows a basic model of an automobile, travelling over horizontal road. The car has...
Figure 1 shows a basic model of an automobile, travelling over horizontal road. The car has a mass M, and a mass moment of inertia Jo= Ma(measured with respect to the center of gravity (c.g)). The vertical displacement of the center of gravity is e(t), and the rotation is e(t) (measured with respect to the position of static equilibrium). The total stiffness at the front wheels is equal to ki and the total stiffness at the rear wheels is ke....
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...
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...
Pre-Lab Assignment 1. Draw separate free-body diagrams for each of the masses from Figure 6.1. Assume...
Pre-Lab Assignment 1. Draw separate free-body diagrams for each of the masses from Figure 6.1. Assume that mi > m2. Figure 6.1 2. Using the free-body diagrams for each mass, m, and m2, develop an equation for the acceleration of the system, in terms of mì, m, and g. Do this by using Newton's second law in the vertical direction to analyze each mass separately. This will give two equations that can be solved for acceleration. Hint: You may find...
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...
Below is a schematic of a double Atwood machine: 1. 2T T m1 T/2 m2 m3 (a) For each of the masses, draw a free body diag...
Below is a schematic of a double Atwood machine: 1. 2T T m1 T/2 m2 m3 (a) For each of the masses, draw a free body diagram (0.5 mark) (b) Write all 4 coupled equations describing the systems (HINT: 3 equations of motion for the 3 masses and 1 equation relating the accelerations) (1.5 marks) (c) Write the coupled equations from above into a matrix (HINT: look at Week 3 Physics content lecture slides) (1 mark) (d) Row reduce your...
Figure 1 shows a system with two masses of which the origins are set up for the springs of \(k_{1}, k_{2}\), and \(k_{3}\) to be unstretched. The system is excited by the base motion of \(x_{b}(t)\).(a) By drawing the FBDs of the two masses and applying the Newton's \(2^{n d}\) Law of Motion, find a matrix equation of motion.(b) Find the undamped, natural frequencies and the corresponding mode shapes of the system for the given system parameters of \(k_{1}=k_{2}=k_{3}=100 \mathrm{kN}...
Page 5 Atwood's Machine Problem 2: Setup an Atwood machine using a pulley, string and two...
Page 5 Atwood's Machine Problem 2: Setup an Atwood machine using a pulley, string and two masses. Measure the acceleration of the masses when released from rest and compare to the theoretical value as calculated in Lesson notes. By measuring the elapsed time, and the vertical displacement Ay, the acceleration y, t ep is determined usingAact Compare the measured and theoretical values of a using the percent error formula (see Lesson 6 for aeory). y2 t Table 1: Experimental Data...
How to answer all of this? Soalan Consider a particle attached to a spring executing a...
How to answer all of this?
Soalan Consider a particle attached to a spring executing a motion x Asin(ot +0) with A 0.32 m,t 0, x= -0.07 m and a velocity -2 m/s. The total energy is 5.6 J.Determine, A-0324 Pertimbangkan partike! yang dipasangkan pada pegar melakranakan gerakan xAsin (at0 dengan A 0.32 m, 0 a berada pada x = 0.07 m dan halaju-2 m/ V=-L Jumlah tenaga adalah 5.6 J. Tentukan (i) phase, 0.22 a fasa e (5 Marks/Markah)...
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...
Figure 1 shows a basic model of an automobile, travelling over horizontal road. The car has a mass M, and a mass moment of inertia Jo= Ma(measured with respect to the center of gravity (c.g)). The vertical displacement of the center of gravity is e(t), and the rotation is e(t) (measured with respect to the position of static equilibrium). The total stiffness at the front wheels is equal to ki and the total stiffness at the rear wheels is ke....
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...
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...
Pre-Lab Assignment 1. Draw separate free-body diagrams for each of the masses from Figure 6.1. Assume that mi > m2. Figure 6.1 2. Using the free-body diagrams for each mass, m, and m2, develop an equation for the acceleration of the system, in terms of mì, m, and g. Do this by using Newton's second law in the vertical direction to analyze each mass separately. This will give two equations that can be solved for acceleration. Hint: You may find...
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...
Below is a schematic of a double Atwood machine: 1. 2T T m1 T/2 m2 m3 (a) For each of the masses, draw a free body diagram (0.5 mark) (b) Write all 4 coupled equations describing the systems (HINT: 3 equations of motion for the 3 masses and 1 equation relating the accelerations) (1.5 marks) (c) Write the coupled equations from above into a matrix (HINT: look at Week 3 Physics content lecture slides) (1 mark) (d) Row reduce your...
Figure 1 shows a system with two masses of which the origins are set up for the springs of \(k_{1}, k_{2}\), and \(k_{3}\) to be unstretched. The system is excited by the base motion of \(x_{b}(t)\).(a) By drawing the FBDs of the two masses and applying the Newton's \(2^{n d}\) Law of Motion, find a matrix equation of motion.(b) Find the undamped, natural frequencies and the corresponding mode shapes of the system for the given system parameters of \(k_{1}=k_{2}=k_{3}=100 \mathrm{kN}...
Page 5 Atwood's Machine Problem 2: Setup an Atwood machine using a pulley, string and two masses. Measure the acceleration of the masses when released from rest and compare to the theoretical value as calculated in Lesson notes. By measuring the elapsed time, and the vertical displacement Ay, the acceleration y, t ep is determined usingAact Compare the measured and theoretical values of a using the percent error formula (see Lesson 6 for aeory). y2 t Table 1: Experimental Data...
How to answer all of this?
Soalan Consider a particle attached to a spring executing a motion x Asin(ot +0) with A 0.32 m,t 0, x= -0.07 m and a velocity -2 m/s. The total energy is 5.6 J.Determine, A-0324 Pertimbangkan partike! yang dipasangkan pada pegar melakranakan gerakan xAsin (at0 dengan A 0.32 m, 0 a berada pada x = 0.07 m dan halaju-2 m/ V=-L Jumlah tenaga adalah 5.6 J. Tentukan (i) phase, 0.22 a fasa e (5 Marks/Markah)...
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