0,T Figure 2. One degree of freedom torsional system.
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2. Consider the torsional system shown in Figure 2. Assume damping is negligible, i.e., ok/J. Fro...
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.
4. Consider the rotational system shown below. For steel, G- 8.27 x 101° Nt/m2 and p 7800 kg/m', ...
4. Consider the rotational system shown below. For steel, G- 8.27 x 101° Nt/m2 and p 7800 kg/m', and for the fluid, μ = 0.309 Nt-sec/m2. Given dı = 0.01m, d,-0.40m, Li-0.50m, L2 = 0.30m and h-0.2mm. a). find the torsional stiffiness K, of the shaft; b). find the moment of inertia J of the steel rotor; c). find the torsional damping constant B, ignoring the viscous effects of the oil on the left and right ends of the rotor....
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...
please solve it as soon as possible and be sure of your answers A cylinder of mass m and mass moment of inertia J is free to roll without slipping but is restrained by 3 springs of stiffinesses k....
please solve it as soon as possible and be sure of
your answers
A cylinder of mass m and mass moment of inertia J is free to roll without slipping but is restrained by 3 springs of stiffinesses k. If the translational and angular displacements of the cylinder are x and 8 from its equilibrium position. Determine the following: a- Equation o method b- Find the natural frequency of vibration f motion of the system assuming that the system is...
QUESTION 10 Q8 (a): shock absorber for a car is to be designed. The system can be considered as simple SDOP system with a mass of m kg as shown in figure (below) and its damped free vibration res...
QUESTION 10 Q8 (a): shock absorber for a car is to be designed. The system can be considered as simple SDOP system with a mass of m kg as shown in figure (below) and its damped free vibration response is shown beside that. The damped period of vibration is to be Td sec. n u It is observed that the amplitude reduced to,% of initial value after 2 oscillations. x(o) 2 For the above question, determine the damped natural frequencies...
Problem Consider the system shown in Figure 5–74(a). The damping ratio of this system is 0.158...
Problem Consider the system shown in Figure 5–74(a). The damping ratio of this system is 0.158 and the undamped natural frequency is 3.16 rad/sec. To improve the relative stability, we employ tachometer feedback. Figure 5–74(b) shows such a tachometer-feedback system. Determine the value of Kn so that the damping ratio of the system is 0.5. Draw unit-step response curves of both the original and tachometer-feedback systems. Also draw the error-versus-time curves for the unit-ramp response of both systems. R(3) C(s)...
A vibratory system can be modeled as a mass spring dashpot system as shown in Figure. In a free vibration test, the mas...
A vibratory system can be modeled as a mass spring dashpot system as shown in Figure. In a free vibration test, the mass is disturbed from its equilibrium position. The corresponding time history plot is given as shown by the plot. Determine the following characteristics of the system: a) The natural frequency of the system b) The effective spring stifness c) The viscous damping coefficient c E 2 20kg 1.5 time (s)
A vibratory system can be modeled as a...
3.10 (Motor drive) Consider a system consisting of a motor driving two masses that are connected...
3.10 (Motor drive) Consider a system consisting of a motor driving two masses that are connected by a torsional spring, as shown in the diagram below. Motor This system can represent a motor with a flexible shaft that drives a load. Assuming that the motor delivers a torque that is proportional to the current I, the dynamics of the system can be described by the equations dt dt (3.43) dtdt where Ф1 and P2 are the angles of the two...
Question B A machine on a viscoelastic foundation (Figure 31.1), modelled as a spring mass-damper system...
Question B A machine on a viscoelastic foundation (Figure 31.1), modelled as a spring mass-damper system is acted upon by a force modelled as a harmonic force: F(t) = 0.2 sin(wt) Force is given in N and time in seconds. W Figure 31.1 Nos Given numerical values: m = 10 kg C=5 M k = 1000 = 1) draw the correct Free-Body-Diagram and determine the equation of motion [2 marks) 2) determine the natural frequency and the damping ratio of...
Consider the rotational system with angular velocity "Ω(t)" and input torque "T(t)." TC From Newton's Law, the equation of motion is J Ω(t)-B. Ω(t) Now suppose that this input to...
Consider the rotational system with angular velocity "Ω(t)" and input torque "T(t)." TC From Newton's Law, the equation of motion is J Ω(t)-B. Ω(t) Now suppose that this input torque is supplied by an electric motor Specifically, T(t) T(t) -Kamp Vin(t) where 1) "Vin is the input voltage supplied to the motor N-m 2) "Kamp" is the motor gain (this constant has units of Volt) So, the transfer function for this system is (s)Kamp The moment of inertia is known...
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.
4. Consider the rotational system shown below. For steel, G- 8.27 x 101° Nt/m2 and p 7800 kg/m', and for the fluid, μ = 0.309 Nt-sec/m2. Given dı = 0.01m, d,-0.40m, Li-0.50m, L2 = 0.30m and h-0.2mm. a). find the torsional stiffiness K, of the shaft; b). find the moment of inertia J of the steel rotor; c). find the torsional damping constant B, ignoring the viscous effects of the oil on the left and right ends of the rotor....
please solve it as soon as possible and be sure of
your answers
A cylinder of mass m and mass moment of inertia J is free to roll without slipping but is restrained by 3 springs of stiffinesses k. If the translational and angular displacements of the cylinder are x and 8 from its equilibrium position. Determine the following: a- Equation o method b- Find the natural frequency of vibration f motion of the system assuming that the system is...
QUESTION 10 Q8 (a): shock absorber for a car is to be designed. The system can be considered as simple SDOP system with a mass of m kg as shown in figure (below) and its damped free vibration response is shown beside that. The damped period of vibration is to be Td sec. n u It is observed that the amplitude reduced to,% of initial value after 2 oscillations. x(o) 2 For the above question, determine the damped natural frequencies...
Problem Consider the system shown in Figure 5–74(a). The damping ratio of this system is 0.158 and the undamped natural frequency is 3.16 rad/sec. To improve the relative stability, we employ tachometer feedback. Figure 5–74(b) shows such a tachometer-feedback system. Determine the value of Kn so that the damping ratio of the system is 0.5. Draw unit-step response curves of both the original and tachometer-feedback systems. Also draw the error-versus-time curves for the unit-ramp response of both systems. R(3) C(s)...
A vibratory system can be modeled as a mass spring dashpot system as shown in Figure. In a free vibration test, the mass is disturbed from its equilibrium position. The corresponding time history plot is given as shown by the plot. Determine the following characteristics of the system: a) The natural frequency of the system b) The effective spring stifness c) The viscous damping coefficient c E 2 20kg 1.5 time (s)
A vibratory system can be modeled as a...
3.10 (Motor drive) Consider a system consisting of a motor driving two masses that are connected by a torsional spring, as shown in the diagram below. Motor This system can represent a motor with a flexible shaft that drives a load. Assuming that the motor delivers a torque that is proportional to the current I, the dynamics of the system can be described by the equations dt dt (3.43) dtdt where Ф1 and P2 are the angles of the two...
Question B A machine on a viscoelastic foundation (Figure 31.1), modelled as a spring mass-damper system is acted upon by a force modelled as a harmonic force: F(t) = 0.2 sin(wt) Force is given in N and time in seconds. W Figure 31.1 Nos Given numerical values: m = 10 kg C=5 M k = 1000 = 1) draw the correct Free-Body-Diagram and determine the equation of motion [2 marks) 2) determine the natural frequency and the damping ratio of...
Consider the rotational system with angular velocity "Ω(t)" and input torque "T(t)." TC From Newton's Law, the equation of motion is J Ω(t)-B. Ω(t) Now suppose that this input torque is supplied by an electric motor Specifically, T(t) T(t) -Kamp Vin(t) where 1) "Vin is the input voltage supplied to the motor N-m 2) "Kamp" is the motor gain (this constant has units of Volt) So, the transfer function for this system is (s)Kamp The moment of inertia is known...
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