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2. For the system shown below, where ki k2-120 N/m, k 150 N/m mi-3kg, m2-5kg and...
2. For the following 3-DOF spring-mass system: (a) Derive the equations of motion. (b) Assuming ki-k2-k3-k...
2. For the following 3-DOF spring-mass system: (a) Derive the equations of motion. (b) Assuming ki-k2-k3-k and mi-m2-m3-m, determine the natural frequencies and mode shapes. rt
MEMB343 MECHANICAL VIBRATIONS ASSIGNMENT l. For the system shown in Figure 1, where mi=5 kg, m,-10 kg, ki=1000 N/m, k2-500 N/m, k, 2000 N/m, fi-100sin(15t) N and f-0, use modal analysis to determine...
MEMB343 MECHANICAL VIBRATIONS ASSIGNMENT l. For the system shown in Figure 1, where mi=5 kg, m,-10 kg, ki=1000 N/m, k2-500 N/m, k, 2000 N/m, fi-100sin(15t) N and f-0, use modal analysis to determine the amplitudes of masses m, and m2. The equations of motion are given as sin(15t), wth natura frequencies 5 01[i, 0 10 500-500x, 500 2500jx, x,[100 ω,-14.14 rad's and a, = 18.71 rad/s, and mode shapes, Φ',, and Φ' k, Im Figure 1
MEMB343 MECHANICAL VIBRATIONS ASSIGNMENT...
3. Consider the spring - mass system shown below, consisting of two masses mi and m2 sus- pended ...
3. Consider the spring - mass system shown below, consisting of two masses mi and m2 sus- pended from springs with spring constants ki and k2, respectively. Assume that there is no damping in the system. a) Show that the displacements ai and r2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above result to show that the spring-mass system satisfies the following fourth order differential equation and c) Find the general solution...
Mi k2 b yi m2 Figure 5-45 Mechanical system. Assuming that mi 10 kg, m2 5 kg, b 10 N-s/m, k 40 N/...
mi k2 b yi m2 Figure 5-45 Mechanical system. Assuming that mi 10 kg, m2 5 kg, b 10 N-s/m, k 40 N/m, and k 20 N/m and that input force u is a constant force of 5 N, obtain the response of the sys- tem. Plot the response curves n(t) versus r and y2(t) versus t with MATLAB Problem B-5-23 Consider the system shown in Figure 5-45. The system is at rest for t < 0. The dis placements...
Problem 1: For the mechanical system shown below, m-2 kg, b-2 N/(m/s). ki 10N/m, k2-2N/m, k3...
Problem 1: For the mechanical system shown below, m-2 kg, b-2 N/(m/s). ki 10N/m, k2-2N/m, k3 8N/m. u(t)2 1(t) is the input of the system and the displacement of the mass, z1(t) is the output. a. b. c. Find the governing equations of the system Find the state space model (matrices, A, B. C, D) Will you see any oscillation in the trajectory of the displacement a? Explain while using the eigenvalues of the system matrix. Hint. Eigen values of...
Problem #5: Transfer Function: Mechanical System 3 2. Variables: Mass terms; mi, m2 Damping term; b1...
Problem #5: Transfer Function: Mechanical System 3 2. Variables: Mass terms; mi, m2 Damping term; b1 Stiffness terms; ki, k2, k3 Friction term; f Write the equations of motion from applying the law of physics to the system Write Transfer Function, Y(s)/X1(s) a) b)
Question 1-4 is about the following mechanical system: Data: ki-20 [N/m] b-2 [Ns/m] k2# 10 [N/m] m2 At) mi Question 1 X...
Question 1-4 is about the following mechanical system: Data: ki-20 [N/m] b-2 [Ns/m] k2# 10 [N/m] m2 At) mi Question 1 X1(s) Develop the symbolic transfer function G1(s)2 F(s) 1.1 Determine the differential equation, that this transfer function describe 1.2 Question 2 Sketch the step response for G1(s), using Matlab and explain the process 2.1 Sketch the pole /zero diagram for the transfer function G1(s) and reflect on the relation between the step response and the pole /zero diagram 2.2...
For the above problem, determine the First Natural Frequency, W1 of the system, in rad/s: 3,0x40,...
For the above problem, determine the First Natural Frequency, W1 of the system, in rad/s: 3,0x40,Nmk7-0.9x103 Nim, k3-35x103 Nim, mrl-3.0 kg and m2 = 3.0 kg Take k For the above problem, determine the Ratio of the Normal Modes for the Second Natural Frequency, r 2 using 2 Take ky-8.25x103 N/m, k2 1,.35-103 N/m, k3-6.25-103 Nim, my-0.5 kg and m2-10 kg ystem shown below, where kjk2. k3 and k4 are stiffnesses of the given springs kFi(t) m2 ms Point 1...
3.15 The mechanical system of Figure 3,56 is formed of a point mass m-Oll and two...
3.15 The mechanical system of Figure 3,56 is formed of a point mass m-Oll and two springs of stiffnesses ki - 100 N/m and k2 120 N/m. Its natra frequency is evaluated by means of a cantilever sensor, which is attached to the point mass. Knowing the cantilever has a constant circular cross section, a length 1 0.08 m, the cantilever's Young's modulus is E -200 GPa, and mass density is p 7600 kg/m3, determine its diameter d, such that...
h 1 (25 Pts) Consider the system shown below C2. C1 ki k2 ky ka kı...
h 1 (25 Pts) Consider the system shown below C2. C1 ki k2 ky ka kı = 8 N/m, k,-100 N/m, k3-k,-50 N/m and c,-c2-16Ns/m. a) Determine the equation of motion for the system b) Compute the time constant and natural frequency of oscillation tain the free response for the initial conditions x(0)-1 and (0)-1
2. For the following 3-DOF spring-mass system: (a) Derive the equations of motion. (b) Assuming ki-k2-k3-k and mi-m2-m3-m, determine the natural frequencies and mode shapes. rt
MEMB343 MECHANICAL VIBRATIONS ASSIGNMENT l. For the system shown in Figure 1, where mi=5 kg, m,-10 kg, ki=1000 N/m, k2-500 N/m, k, 2000 N/m, fi-100sin(15t) N and f-0, use modal analysis to determine the amplitudes of masses m, and m2. The equations of motion are given as sin(15t), wth natura frequencies 5 01[i, 0 10 500-500x, 500 2500jx, x,[100 ω,-14.14 rad's and a, = 18.71 rad/s, and mode shapes, Φ',, and Φ' k, Im Figure 1
MEMB343 MECHANICAL VIBRATIONS ASSIGNMENT...
3. Consider the spring - mass system shown below, consisting of two masses mi and m2 sus- pended from springs with spring constants ki and k2, respectively. Assume that there is no damping in the system. a) Show that the displacements ai and r2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above result to show that the spring-mass system satisfies the following fourth order differential equation and c) Find the general solution...
mi k2 b yi m2 Figure 5-45 Mechanical system. Assuming that mi 10 kg, m2 5 kg, b 10 N-s/m, k 40 N/m, and k 20 N/m and that input force u is a constant force of 5 N, obtain the response of the sys- tem. Plot the response curves n(t) versus r and y2(t) versus t with MATLAB Problem B-5-23 Consider the system shown in Figure 5-45. The system is at rest for t < 0. The dis placements...
Problem 1: For the mechanical system shown below, m-2 kg, b-2 N/(m/s). ki 10N/m, k2-2N/m, k3 8N/m. u(t)2 1(t) is the input of the system and the displacement of the mass, z1(t) is the output. a. b. c. Find the governing equations of the system Find the state space model (matrices, A, B. C, D) Will you see any oscillation in the trajectory of the displacement a? Explain while using the eigenvalues of the system matrix. Hint. Eigen values of...
Problem #5: Transfer Function: Mechanical System 3 2. Variables: Mass terms; mi, m2 Damping term; b1 Stiffness terms; ki, k2, k3 Friction term; f Write the equations of motion from applying the law of physics to the system Write Transfer Function, Y(s)/X1(s) a) b)
Question 1-4 is about the following mechanical system: Data: ki-20 [N/m] b-2 [Ns/m] k2# 10 [N/m] m2 At) mi Question 1 X1(s) Develop the symbolic transfer function G1(s)2 F(s) 1.1 Determine the differential equation, that this transfer function describe 1.2 Question 2 Sketch the step response for G1(s), using Matlab and explain the process 2.1 Sketch the pole /zero diagram for the transfer function G1(s) and reflect on the relation between the step response and the pole /zero diagram 2.2...
For the above problem, determine the First Natural Frequency, W1 of the system, in rad/s: 3,0x40,Nmk7-0.9x103 Nim, k3-35x103 Nim, mrl-3.0 kg and m2 = 3.0 kg Take k For the above problem, determine the Ratio of the Normal Modes for the Second Natural Frequency, r 2 using 2 Take ky-8.25x103 N/m, k2 1,.35-103 N/m, k3-6.25-103 Nim, my-0.5 kg and m2-10 kg ystem shown below, where kjk2. k3 and k4 are stiffnesses of the given springs kFi(t) m2 ms Point 1...
3.15 The mechanical system of Figure 3,56 is formed of a point mass m-Oll and two springs of stiffnesses ki - 100 N/m and k2 120 N/m. Its natra frequency is evaluated by means of a cantilever sensor, which is attached to the point mass. Knowing the cantilever has a constant circular cross section, a length 1 0.08 m, the cantilever's Young's modulus is E -200 GPa, and mass density is p 7600 kg/m3, determine its diameter d, such that...
h 1 (25 Pts) Consider the system shown below C2. C1 ki k2 ky ka kı = 8 N/m, k,-100 N/m, k3-k,-50 N/m and c,-c2-16Ns/m. a) Determine the equation of motion for the system b) Compute the time constant and natural frequency of oscillation tain the free response for the initial conditions x(0)-1 and (0)-1
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