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The landing gear of an airplane can be idealised as the spring-mass-damper system shown in the...
Design a PD controller for mass-spring systems by the Root-Locus Method Mass 2.6Kg Spring stiffness 200N/m Zero Damp...
Design a PD controller for mass-spring systems by the Root-Locus Method Mass 2.6Kg Spring stiffness 200N/m Zero Damper Input: force Output: mass displacement, y Design a PD controller, Kp+ Kd*s, for vibration reduction by root-locus method so that the damping ratio of the closed-loop systems is 0.5 and natural frequency is 3 rad/s Transfer Function of closed-loop system Draw root locus plot Design gains ww
Design a PD controller for mass-spring systems by the Root-Locus Method Mass 2.6Kg Spring stiffness...
QUESTION 4 (140 marks) Determine the damped frequency of the spring-mass system schematically illustrated below if...
QUESTION 4 (140 marks) Determine the damped frequency of the spring-mass system schematically illustrated below if the spring stiffness is 3000 N/m and the damping coefficient c is set at 320 Ns/m. If a periodic 260 N force is applied to the mass at a frequency of 2 Hz, determine the amplitude of the forced vibration. Spring Viscous damper 35 kg Figure 4
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.
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...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a s...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mx+cx + kx = A sin(at) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor 5 and the un-damped natural frequency Using the given formulas for...
2. Consider a spring-mass-damper system with oh-20 rad/s and K-1k = 0.010 mN that is initially...
2. Consider a spring-mass-damper system with oh-20 rad/s and K-1k = 0.010 mN that is initially at rest [y(0) = dydt(0)-0]. This systern is subjected to a step load F-10 N at t-0·Plot displacement y(t) for range 0StS0.8 for 3 different damping ratios(-0.40,1.00, 1.60) on a single graph (see Eq. 3.15). Use a software package to plot (Excel, MathCad, Matlab, etc.)-do not plot by hand. (12 points)
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...
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...
QUESTION 27 020 The rotor of a steam turbine with mass 10.5 kg is mounted on steel shaft (E- 207 GPa). The shaft diameter is 49 mm and is 1.8 m long. The shaft is suppored at the two ends by the...
QUESTION 27 020 The rotor of a steam turbine with mass 10.5 kg is mounted on steel shaft (E- 207 GPa). The shaft diameter is 49 mm and is 1.8 m long. The shaft is suppored at the two ends by the bearings The turbine rotor has an eccentricity of 9.0 mm and operates at T200 rpm (754.0 rad/s). Determine the natural frequency of the system in rad/s Rotor Ο 214.279 rads 50985.64 rad o 45915.49 ad/s 484424 rad/s QUESTION...
Problem Set A Problem 6. (20%) A ordinary differential equation for a mass-damper-spring system is following....
Problem Set A Problem 6. (20%) A ordinary differential equation for a mass-damper-spring system is following. The mass m 1, damping coetfic e initial position y(o) O, and the initial velocity i constant k 3 and force 10, all are in appropriate units. Th 1, spring zero, within the time range of O to 20 unit of time, use Matlab find the solution of function y(t)? Hint: you need to convert the 2nd order ODE into two 1st order ODEs....
Design a PD controller for mass-spring systems by the Root-Locus Method Mass 2.6Kg Spring stiffness 200N/m Zero Damper Input: force Output: mass displacement, y Design a PD controller, Kp+ Kd*s, for vibration reduction by root-locus method so that the damping ratio of the closed-loop systems is 0.5 and natural frequency is 3 rad/s Transfer Function of closed-loop system Draw root locus plot Design gains ww
Design a PD controller for mass-spring systems by the Root-Locus Method Mass 2.6Kg Spring stiffness...
QUESTION 4 (140 marks) Determine the damped frequency of the spring-mass system schematically illustrated below if the spring stiffness is 3000 N/m and the damping coefficient c is set at 320 Ns/m. If a periodic 260 N force is applied to the mass at a frequency of 2 Hz, determine the amplitude of the forced vibration. Spring Viscous damper 35 kg Figure 4
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.
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mx+cx + kx = A sin(at) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor 5 and the un-damped natural frequency Using the given formulas for...
2. Consider a spring-mass-damper system with oh-20 rad/s and K-1k = 0.010 mN that is initially at rest [y(0) = dydt(0)-0]. This systern is subjected to a step load F-10 N at t-0·Plot displacement y(t) for range 0StS0.8 for 3 different damping ratios(-0.40,1.00, 1.60) on a single graph (see Eq. 3.15). Use a software package to plot (Excel, MathCad, Matlab, etc.)-do not plot by hand. (12 points)
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...
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...
QUESTION 27 020 The rotor of a steam turbine with mass 10.5 kg is mounted on steel shaft (E- 207 GPa). The shaft diameter is 49 mm and is 1.8 m long. The shaft is suppored at the two ends by the bearings The turbine rotor has an eccentricity of 9.0 mm and operates at T200 rpm (754.0 rad/s). Determine the natural frequency of the system in rad/s Rotor Ο 214.279 rads 50985.64 rad o 45915.49 ad/s 484424 rad/s QUESTION...
Problem Set A Problem 6. (20%) A ordinary differential equation for a mass-damper-spring system is following. The mass m 1, damping coetfic e initial position y(o) O, and the initial velocity i constant k 3 and force 10, all are in appropriate units. Th 1, spring zero, within the time range of O to 20 unit of time, use Matlab find the solution of function y(t)? Hint: you need to convert the 2nd order ODE into two 1st order ODEs....
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