THIS IS THE ANSWER OF PROBLEM 8.2 WHICH I HAD TO FIND THE MASS, STIFFNESS, AND DAMPING MATRICES FOR THE PENDULUM CART.
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THIS IS THE ANSWER OF PROBLEM 8.2 WHICH I HAD TO FIND
THE MASS, STIFFNESS, AND...
For the following 2DOF linear mass-spring-damper system r2 (t) M-2kg K -18N/m C- 1.2N s/m i(t) - ...
For the following 2DOF linear mass-spring-damper system r2 (t) M-2kg K -18N/m C- 1.2N s/m i(t) - 5 sin 2t (N) f2(t)-t (N) l. Formulate an IVP for vibration analysis in terms of xi (t) and x2(t) in a matrix form. Assume that the 2. Solve an eigenvalue problem to find the natural frequencies and modeshape vectors of the system 3. What is the modal matrix of the system? Verify the orthogonal properties of the modal matrix, Ф, with system...
Answer last four questions 1. A spring-mass-damper system has mass of 150 kg, stiffness of 1500...
Answer last four questions
1. A spring-mass-damper system has mass of 150 kg, stiffness of 1500 N/m and damping coefficient of 200 kg/s. i) Calculate the undamped natural frequency ii) Calculate the damping ratio iii) Calculate the damped natural frequency iv) Is the system overdamped, underdamped or critically damped? v) Does the solution oscillate? The system above is given an initial velocity of 10 mm/s and an initial displacement of -5 mm. vi) Calculate the form of the response and...
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...
Problem 2: Cart Standard Pendulum Model Consider the cart standard pendulum system shown in Figur...
Problem 2: Cart Standard Pendulum Model Consider the cart standard pendulum system shown in Figure 1 with parameters given in Table 1 I C.8 I Ig Figure 1: Cart Standard Pendulum Schematic Syb Definition Unit Variablesr osition of the cart angle that the force applied on cart (control) mass of the cart mass ot t 123 lum makes with the vertic Parameters M5 kg utm 0.5 location of the c.g. of the pendulum above the 4 = m moment of...
Problem: Find the natural frequencies of the system shown in Figure. Take m 2 kg ma 2.5 kg ms 3.0...
Problem: Find the natural frequencies of the system shown in Figure. Take m 2 kg ma 2.5 kg ms 3.0 kg me = 1.5 kg 914 Given: Four degree of freedom spring-mass system with given masses an stiffnesses. Find: Natural frequencies and mode shapes. Approach: Find the eigenvalues and eigenvectors of the dynamical matrix. 1. Determine [m] and [k] matrices of the vibrating system with all details 2. Determine [DI matrix. 3. Determine Natural frequencies and mode shapes analytically 3....
Figure 5 shows a pick-up truck of a total mass mi transporting a small cart of a mass m2. The sma...
Figure 5 shows a pick-up truck of a total mass mi transporting a small cart of a mass m2. The small cart is hitched through two springs of axial stiffness k each to the truck (b) body. Absolute displacement of the truck is xi while that of the cart is x2 (i) Find the relative motion (n-m) of the cart when the truck is subjected to a (7 marks) Find the natural frequencies and mode shapes of this two-degree-of-freedom harmonic...
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.
Please derive the equations and draw simulink model. For the vibration absorber model below. (a) ma is selected to be 5% of main mass m, what should the value of ka be so the vibration of the main...
Please derive the equations and draw simulink
model.
For the vibration absorber model below. (a) ma is selected to be 5% of main mass m, what should the value of ka be so the vibration of the main mass is eliminated? (b) What are the natural frequencies of the system? (c) Adding a damper to the absorber such that the absorber has a damping ratio of 0.5, how much would the main mass vibrate now? What if the excitation frequency...
HZ A mass of 0.4 kg is suspended from a spring of stiffness 0.4 N/mm. The...
HZ A mass of 0.4 kg is suspended from a spring of stiffness 0.4 N/mm. The damping is 3.794733192 kg/s What is the undamped natural frequency of the system in Hz? f= Your answer should be accurate to within +/-0.1. What is the value of the critical damping coefficient? Сст в kg/s Your answer should be accurate to within +/-0.1. What is the value of the damping ratio? Your answer should be accurate to within +/-0.01. Is the system: (a)...
I. (20%) A frame structure with lumped mass is shown below: 3m L/2 m El El It can be shown that t...
Please provide a clear step by step solution.
I. (20%) A frame structure with lumped mass is shown below: 3m L/2 m El El It can be shown that the stiffness and mass matrices of the framed structure with respect to the coordinates u and u2 can be obtained as: 4 01 [A]=7713 41 [M-m and L424J (a) Determine the natural frequencies and modal vectors of the structural system. (b) Assume the first modal vector is estimated as迪 . Use...
For the following 2DOF linear mass-spring-damper system r2 (t) M-2kg K -18N/m C- 1.2N s/m i(t) - 5 sin 2t (N) f2(t)-t (N) l. Formulate an IVP for vibration analysis in terms of xi (t) and x2(t) in a matrix form. Assume that the 2. Solve an eigenvalue problem to find the natural frequencies and modeshape vectors of the system 3. What is the modal matrix of the system? Verify the orthogonal properties of the modal matrix, Ф, with system...
Answer last four questions
1. A spring-mass-damper system has mass of 150 kg, stiffness of 1500 N/m and damping coefficient of 200 kg/s. i) Calculate the undamped natural frequency ii) Calculate the damping ratio iii) Calculate the damped natural frequency iv) Is the system overdamped, underdamped or critically damped? v) Does the solution oscillate? The system above is given an initial velocity of 10 mm/s and an initial displacement of -5 mm. vi) Calculate the form of the response and...
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...
Problem 2: Cart Standard Pendulum Model Consider the cart standard pendulum system shown in Figure 1 with parameters given in Table 1 I C.8 I Ig Figure 1: Cart Standard Pendulum Schematic Syb Definition Unit Variablesr osition of the cart angle that the force applied on cart (control) mass of the cart mass ot t 123 lum makes with the vertic Parameters M5 kg utm 0.5 location of the c.g. of the pendulum above the 4 = m moment of...
Problem: Find the natural frequencies of the system shown in Figure. Take m 2 kg ma 2.5 kg ms 3.0 kg me = 1.5 kg 914 Given: Four degree of freedom spring-mass system with given masses an stiffnesses. Find: Natural frequencies and mode shapes. Approach: Find the eigenvalues and eigenvectors of the dynamical matrix. 1. Determine [m] and [k] matrices of the vibrating system with all details 2. Determine [DI matrix. 3. Determine Natural frequencies and mode shapes analytically 3....
Figure 5 shows a pick-up truck of a total mass mi transporting a small cart of a mass m2. The small cart is hitched through two springs of axial stiffness k each to the truck (b) body. Absolute displacement of the truck is xi while that of the cart is x2 (i) Find the relative motion (n-m) of the cart when the truck is subjected to a (7 marks) Find the natural frequencies and mode shapes of this two-degree-of-freedom harmonic...
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.
Please derive the equations and draw simulink
model.
For the vibration absorber model below. (a) ma is selected to be 5% of main mass m, what should the value of ka be so the vibration of the main mass is eliminated? (b) What are the natural frequencies of the system? (c) Adding a damper to the absorber such that the absorber has a damping ratio of 0.5, how much would the main mass vibrate now? What if the excitation frequency...
HZ A mass of 0.4 kg is suspended from a spring of stiffness 0.4 N/mm. The damping is 3.794733192 kg/s What is the undamped natural frequency of the system in Hz? f= Your answer should be accurate to within +/-0.1. What is the value of the critical damping coefficient? Сст в kg/s Your answer should be accurate to within +/-0.1. What is the value of the damping ratio? Your answer should be accurate to within +/-0.01. Is the system: (a)...
Please provide a clear step by step solution.
I. (20%) A frame structure with lumped mass is shown below: 3m L/2 m El El It can be shown that the stiffness and mass matrices of the framed structure with respect to the coordinates u and u2 can be obtained as: 4 01 [A]=7713 41 [M-m and L424J (a) Determine the natural frequencies and modal vectors of the structural system. (b) Assume the first modal vector is estimated as迪 . Use...
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