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A single dof vibration system, modeled by a mass of 50 kg, damping coefficient of 300...
An automobile suspension system is modeled as a 2-DoF vibration system as shown in Figure below...
An automobile suspension system is modeled as a 2-DoF
vibration system as shown in Figure below
Derive the equation of motion
Determine the natural frequencies of the automobile
with the following data
Mass (mm) = 1000kg1000kg
Momen of inertia (ImIm) = 450kgm2450kgm2
Distance between front axle and C.G. (LfLf) =
1.2m1.2m
Distance between rear axle and C.G. (LfLf) =
1.5m1.5m
Front spring stiffnes (kfkf) = 18kN/m18kN/m
Rear spring stiffnes (krkr) = 17kN/m17kN/m
Front damper coefficient (cfcf) =
3kNs/m3kNs/m
Rear damper...
A vibration isolation system for a 1-DOF mechanical system is shown below. Displacement of the mass...
A vibration isolation system for a 1-DOF mechanical system is shown below. Displacement of the mass x is measured from the static equilibrium position and the system parameters are m = 0.3 kg. k=10N/m, b = 4.4 Ns/m, and by = 0.5 Ns/m. Fixed 1. TI W Fixed base Figure / sehen voulon tem a) Derive the mathematical model of the system. Make sure you have the FBD and all equations and signs are properly showcased. b) Use the system...
> DOF Free Vibration An o rweligible mass and length move in the vertical plane by...
> DOF Free Vibration An o rweligible mass and length move in the vertical plane by spring and massen hux - 100 min the mass and length is pivoted at the middle point and 18 and masseo, shown. I - 123 m h Bite the Equations of Motion in Matrix Form ind the natural frequencies Find the mode shapes
A damped system consists of a mass (m = 30kg) supported on a spring and a...
A damped system consists of a mass (m = 30kg) supported on a spring and a damper in parallel. In an experiment, the period of vibration of this system was measured to be 0.5 seconds, and the ratio of maximum displacement between two successive cycles was determined from the experimental data to be 20. Determine: a. The logarithmic decrement. [2] Q4a. Answer: b. The damping ratio, commenting if this is over-damped, critically damped, or under-damped. [4] Q4b. Answer: c. The...
Consider a single degree of freedom (SDOF) with mass-spring-damper system
Consider a single degree of freedom (SDOF) with mass-spring-damper system subjected to harmonic excitation having the following characteristics: Mass, m = 850 kg; stiffness, k = 80 kN/m; damping constant, c = 2000 N.s/m, forcing function amplitude, f0 = 5 N; forcing frequency, ωt = 30 rad/s. (a) Calculate the steady-state response of the system and state whether the system is underdamped, critically damped, or overdamped. (b) What happen to the steady-state response when the damping is increased to 18000 N.s/m? (Hint: Determine...
Problem 2 (20%) Free Vibration with Velocity Dependent Force. Consider a 1 DOF system consisting of...
Problem 2 (20%) Free Vibration with Velocity Dependent Force. Consider a 1 DOF system consisting of a block with mass 2 kg hanging from a spring with stiffness 100 N/m. The block is fully immersed in the liquid and based on the properties of the liquid, you have determined experimentally that the drag force (damping force) on the block has a magnitude of 0.91*] where x is velocity and 0.9 has units (Ns/m). Assume positive displacement of the block is...
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...
F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the...
F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the system (state the concepts you use) (b) Write the characteristic equation of the system [4 marks 12 marks (c) What is the category of differential equations does the characteristic equation [2 marks fall into? (d) Prove that the steady state amplitude of vibration of the system is Xk Fo 25 + 0 marks (e) Prove that...
Question 3 (24 marks) A uniform bar of length L= 1.1m and mass m = 4.2kg...
Question 3 (24 marks) A uniform bar of length L= 1.1m and mass m = 4.2kg is connected with a spring with stiffness k = 2000N/m and a damper with damping ratio š = 0.3. The bar is rotating about a point that is 10cm from the left end. (1) Calculate the total kinetic energy and total potential energy. (2) Derive the equation of motion using energy based approach. (3) Determine the undamped natural frequency and damped natural frequency of...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in Fig. II-2. The block is moved to the right of the equilibrium position and is released from rest (time t = 0) when its displacement, x = XO. Using the notations given in Fig. II-2,4 (1) Draw the free body diagram of the block - (2) Write the equation of motion of the block- If the initial displacement of the block to the right...
An automobile suspension system is modeled as a 2-DoF
vibration system as shown in Figure below
Derive the equation of motion
Determine the natural frequencies of the automobile
with the following data
Mass (mm) = 1000kg1000kg
Momen of inertia (ImIm) = 450kgm2450kgm2
Distance between front axle and C.G. (LfLf) =
1.2m1.2m
Distance between rear axle and C.G. (LfLf) =
1.5m1.5m
Front spring stiffnes (kfkf) = 18kN/m18kN/m
Rear spring stiffnes (krkr) = 17kN/m17kN/m
Front damper coefficient (cfcf) =
3kNs/m3kNs/m
Rear damper...
A vibration isolation system for a 1-DOF mechanical system is shown below. Displacement of the mass x is measured from the static equilibrium position and the system parameters are m = 0.3 kg. k=10N/m, b = 4.4 Ns/m, and by = 0.5 Ns/m. Fixed 1. TI W Fixed base Figure / sehen voulon tem a) Derive the mathematical model of the system. Make sure you have the FBD and all equations and signs are properly showcased. b) Use the system...
> DOF Free Vibration An o rweligible mass and length move in the vertical plane by spring and massen hux - 100 min the mass and length is pivoted at the middle point and 18 and masseo, shown. I - 123 m h Bite the Equations of Motion in Matrix Form ind the natural frequencies Find the mode shapes
A damped system consists of a mass (m = 30kg) supported on a spring and a damper in parallel. In an experiment, the period of vibration of this system was measured to be 0.5 seconds, and the ratio of maximum displacement between two successive cycles was determined from the experimental data to be 20. Determine: a. The logarithmic decrement. [2] Q4a. Answer: b. The damping ratio, commenting if this is over-damped, critically damped, or under-damped. [4] Q4b. Answer: c. The...
Problem 2 (20%) Free Vibration with Velocity Dependent Force. Consider a 1 DOF system consisting of a block with mass 2 kg hanging from a spring with stiffness 100 N/m. The block is fully immersed in the liquid and based on the properties of the liquid, you have determined experimentally that the drag force (damping force) on the block has a magnitude of 0.91*] where x is velocity and 0.9 has units (Ns/m). Assume positive displacement of the block is...
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...
F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the system (state the concepts you use) (b) Write the characteristic equation of the system [4 marks 12 marks (c) What is the category of differential equations does the characteristic equation [2 marks fall into? (d) Prove that the steady state amplitude of vibration of the system is Xk Fo 25 + 0 marks (e) Prove that...
Question 3 (24 marks) A uniform bar of length L= 1.1m and mass m = 4.2kg is connected with a spring with stiffness k = 2000N/m and a damper with damping ratio š = 0.3. The bar is rotating about a point that is 10cm from the left end. (1) Calculate the total kinetic energy and total potential energy. (2) Derive the equation of motion using energy based approach. (3) Determine the undamped natural frequency and damped natural frequency of...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in Fig. II-2. The block is moved to the right of the equilibrium position and is released from rest (time t = 0) when its displacement, x = XO. Using the notations given in Fig. II-2,4 (1) Draw the free body diagram of the block - (2) Write the equation of motion of the block- If the initial displacement of the block to the right...
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