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G c 11 k Uniform bar, mass m Q4|| for the shown figure Find out the...
The figure shows the mass m at the end of a bar of length / is...
The figure shows the mass m at the end of a bar of length / is restrained by a spring and dashpot. The mass is initially at rest and vibrates in the vertical plane under the action of the force F(1). Determine the equation of motion, natural frequency, and damping ratio of the system when m = 45 kg, k = 9700 N/m, c = 950 N.s/m, a - 0.8 m, and I = 2 m. Neglect the mass of...
L. 2 uestion 3 (20 marks) A rotating bar of length L and mass m stiffness k and a damper with dam...
L. 2 uestion 3 (20 marks) A rotating bar of length L and mass m stiffness k and a damper with damping constant gy 2 connected (1) Find the total kinetic energy and total pot of the ystem,e total kinetic edamping constonnected with a spring with system. (2) Derive the equation of motion using e (3) Determine the undamped natural fir 4) Calculate the damping ratio of the sy nergy metho frequency of the system. Gven
L. 2 uestion 3...
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...
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m...
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m = 10 kg, and damping constant c-150 N-s/m. If the initial displacement is xo-o and the initial velocity is 10 m/s (1) Find the damping ratio. (2) Is the system underdamped or overdamped? Why? (3) Calculate the damped natural frequency (4) Determine the free vibration response of the system.
ke Slender bar of mass m As shown in Figure 1, a uniform slender bar with...
ke Slender bar of mass m As shown in Figure 1, a uniform slender bar with mass m and length L is supported by a vertical spring at its right end while a mass block 2m suspended from its left end through a spring is supported by another spring. All these three vertical springs have the same stiffness k. If the downward vertical displacement x of the mass block and the clockwise rotation angle 8 of the bar are assumed...
The figure below shows a uniform slender bar supported by cantilevers at A and C. At B a linear spring with stiffness K' is connected to an additional point mass 'm'. Note the physical pr...
The figure below shows a uniform slender bar supported by cantilevers at A and C. At B a linear spring with stiffness K' is connected to an additional point mass 'm'. Note the physical properties of the bar include cross sectional area A, Young's modulus E, second moment of area I, and, density ρ, and length AB-BC-L. 1. 2. Develop the matrix equation of motion for the FEM system in the model How many natural frequencies are in the system?...
Write the differential equation of motion for the system shown in the figure, and find the...
Write the differential equation of motion for the system shown in the figure, and find the damped natural frequency and damping ratio of this system.
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...
Q1- For the system shown below, with small mass of value (m) and lever of mass...
Q1- For the system shown below, with small mass of value (m) and lever of mass moment of inertia (J). • find equivalent mass, equivalent stiffness, and equivalent damping, all these interms of (x) displacement . Get equation of motion Interms of these equivalent quantities. • Find natural frequency (Wn) and damping ratio (zeta). • Find X(t) when the system condition is critically damping ,,X(0)=M and v(0)=0. tinfring
Problem 5: For the system shown below, write the differential equations for small motions of the ...
Problem 5: For the system shown below, write the differential equations for small motions of the system, in terms of the degrees of freedom (x(t),() Mass of the bar is m, and mass of the block is also m. System is set into motion through suitable initial conditions. Once you find the equations of motion in terms of the respective degrees of freedom, write out the natural frequency and the damping ratio for each sub-system, respectively.
Problem 5: For the...
The figure shows the mass m at the end of a bar of length / is restrained by a spring and dashpot. The mass is initially at rest and vibrates in the vertical plane under the action of the force F(1). Determine the equation of motion, natural frequency, and damping ratio of the system when m = 45 kg, k = 9700 N/m, c = 950 N.s/m, a - 0.8 m, and I = 2 m. Neglect the mass of...
L. 2 uestion 3 (20 marks) A rotating bar of length L and mass m stiffness k and a damper with damping constant gy 2 connected (1) Find the total kinetic energy and total pot of the ystem,e total kinetic edamping constonnected with a spring with system. (2) Derive the equation of motion using e (3) Determine the undamped natural fir 4) Calculate the damping ratio of the sy nergy metho frequency of the system. Gven
L. 2 uestion 3...
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...
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m = 10 kg, and damping constant c-150 N-s/m. If the initial displacement is xo-o and the initial velocity is 10 m/s (1) Find the damping ratio. (2) Is the system underdamped or overdamped? Why? (3) Calculate the damped natural frequency (4) Determine the free vibration response of the system.
ke Slender bar of mass m As shown in Figure 1, a uniform slender bar with mass m and length L is supported by a vertical spring at its right end while a mass block 2m suspended from its left end through a spring is supported by another spring. All these three vertical springs have the same stiffness k. If the downward vertical displacement x of the mass block and the clockwise rotation angle 8 of the bar are assumed...
The figure below shows a uniform slender bar supported by cantilevers at A and C. At B a linear spring with stiffness K' is connected to an additional point mass 'm'. Note the physical properties of the bar include cross sectional area A, Young's modulus E, second moment of area I, and, density ρ, and length AB-BC-L. 1. 2. Develop the matrix equation of motion for the FEM system in the model How many natural frequencies are in the system?...
Write the differential equation of motion for the system shown in the figure, and find the damped natural frequency and damping ratio of this system.
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...
Q1- For the system shown below, with small mass of value (m) and lever of mass moment of inertia (J). • find equivalent mass, equivalent stiffness, and equivalent damping, all these interms of (x) displacement . Get equation of motion Interms of these equivalent quantities. • Find natural frequency (Wn) and damping ratio (zeta). • Find X(t) when the system condition is critically damping ,,X(0)=M and v(0)=0. tinfring
Problem 5: For the system shown below, write the differential equations for small motions of the system, in terms of the degrees of freedom (x(t),() Mass of the bar is m, and mass of the block is also m. System is set into motion through suitable initial conditions. Once you find the equations of motion in terms of the respective degrees of freedom, write out the natural frequency and the damping ratio for each sub-system, respectively.
Problem 5: For the...
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