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(10 pts) Consider the multi degree of freedom system of Fig. I a) Write the equations...
5. (10 pts) Consider the two-mass sy stem of Fig. 1. The system is free to move in x1 plane. a) Derive the equations of motion. b) Identify the mass matrix and the stiffness matrix if the displacemen...
5. (10 pts) Consider the two-mass sy stem of Fig. 1. The system is free to move in x1 plane. a) Derive the equations of motion. b) Identify the mass matrix and the stiffness matrix if the displacement vector is x=1 x, x2 x3 x4 3k 4k 4k
5. (10 pts) Consider the two-mass sy stem of Fig. 1. The system is free to move in x1 plane. a) Derive the equations of motion. b) Identify the mass matrix and...
Consider the multi-degree of freedom system shown in Fig 1. Let the first four spring constants...
Consider the multi-degree of freedom system shown in Fig 1. Let the first four spring constants k; = 1 N/m {i=1,..4}, the final spring constant be kg = 2 N/m, the exterior masses mi = m = 3 kg, and the interior masses m2 = m3 = 1 kg. Jovit cum alv Lampu Milli MÁV DLİNE Derive the set of scalar equations of motion of the system, written in ma- trix/vector form.
- Derive the equations of motion of the system in terms of variables m and K...
- Derive the equations of motion of the system in terms of variables m and K and express them in matrix notation. Finally, express the equations of motion numerically in matrix notations if the stiffness and mass coefficients are k = 1 kip/in and m = 0.15 kip-sec? / in. Use X1, X2, and X: as degrees of freedom. (20 pts) X2 X 3m
Please provide references to the Model/Equations used from the textbook. 1. A Three Degree of Freedom...
Please provide references to the Model/Equations used from the
textbook.
1. A Three Degree of Freedom discretized lumped parameter system is shown in the figure. (a). Derive the equations of motion for the system using Newton's Second Law of Motion or Energy Methods. (b). Transform the ordinary differential equations obtained into the matrix form. (C). Estimate the fundamental frequency of vibration of the system, assuming the mode shape and the following system parameters: ka=k, k2= 2k, k3 = 3k, m1...
Figure Q4 shows a complex multi-degree of freedom spring-mass system. a) Develop the equation of motion...
Figure Q4 shows a complex multi-degree of freedom spring-mass system. a) Develop the equation of motion of the system. (6 Marks) b) If m - m - m - m and k, = kx - kyky+ ks = k, Determine the natural frequencies and mode shape of the system. (16 Marks) c) Estimate the largest strain that can occur to any of the spring in the system. State which spring in your answer. Marks) (8 ka ka ks ma m2...
1. (50 pts) Consider the spin degree of freedom of an electron under an external magnetic...
1. (50 pts) Consider the spin degree of freedom of an electron under an external magnetic field in the r-direction. The spin is initially (at time t 0) in the z-direction. (a) Write down the Hamiltonian for the electron spin. (Do you remember the elementary magnetic moment of electron, the Bohr magneton μΒ, in terms of electron mass me and the elementary charge e?) b) Write down the Schrödinger equation for the spin (c) Describe the motion of spin direction
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...
1. Derive the equations of motion of the system shown in Fig 1 by using Lagrange's...
1. Derive the equations of motion of the system shown in Fig 1 by using Lagrange's equations. Find the natural frequencies and mode shapes of the dynamical system for k 1 N/m, k-2 N/m, k I N/m, and mi 2 kg, m l kg, m -2 kg. scale the eigenvectors matrix Ф in order to achieve a mass normalized eigenvectors matrix Φ such that: F40 Fan Fig. 1
5. Consider the following time-dependent Lagrangian for a system with one degree of freedom , (10)...
5. Consider the following time-dependent Lagrangian for a system with one degree of freedom , (10) where 8, m and k are fixed real constants greater than zero. (total 10 points) (a) Write down the Euler-Lagrange equation of motion for this system, and interpret the resulting equation in terms of a known physical system. (1 point) (b) Find Hamiltonian via Legendre transformation. (1 point) (c) Show that q(t) and the corresponding canonical momentum p(t) can be found as follows for...
For the system shown in Figure 6, a. How many degrees of freedom is this system and why? b. Write the equations of moti...
For the system shown in Figure 6, a. How many degrees of freedom is this system and why? b. Write the equations of motion. For the remainder parts, assume alll the dampers are removed: c. If Ki=K3 and mim3, set the necessary matrix to find the natural frequencies and mode shapes d. For part c above, determine and explain how to get the natural frequencies. m1 Ty Absorber тз k1 С1 k3 m2 C2
For the system shown in Figure...
5. (10 pts) Consider the two-mass sy stem of Fig. 1. The system is free to move in x1 plane. a) Derive the equations of motion. b) Identify the mass matrix and the stiffness matrix if the displacement vector is x=1 x, x2 x3 x4 3k 4k 4k
5. (10 pts) Consider the two-mass sy stem of Fig. 1. The system is free to move in x1 plane. a) Derive the equations of motion. b) Identify the mass matrix and...
Consider the multi-degree of freedom system shown in Fig 1. Let the first four spring constants k; = 1 N/m {i=1,..4}, the final spring constant be kg = 2 N/m, the exterior masses mi = m = 3 kg, and the interior masses m2 = m3 = 1 kg. Jovit cum alv Lampu Milli MÁV DLİNE Derive the set of scalar equations of motion of the system, written in ma- trix/vector form.
- Derive the equations of motion of the system in terms of variables m and K and express them in matrix notation. Finally, express the equations of motion numerically in matrix notations if the stiffness and mass coefficients are k = 1 kip/in and m = 0.15 kip-sec? / in. Use X1, X2, and X: as degrees of freedom. (20 pts) X2 X 3m
Please provide references to the Model/Equations used from the
textbook.
1. A Three Degree of Freedom discretized lumped parameter system is shown in the figure. (a). Derive the equations of motion for the system using Newton's Second Law of Motion or Energy Methods. (b). Transform the ordinary differential equations obtained into the matrix form. (C). Estimate the fundamental frequency of vibration of the system, assuming the mode shape and the following system parameters: ka=k, k2= 2k, k3 = 3k, m1...
Figure Q4 shows a complex multi-degree of freedom spring-mass system. a) Develop the equation of motion of the system. (6 Marks) b) If m - m - m - m and k, = kx - kyky+ ks = k, Determine the natural frequencies and mode shape of the system. (16 Marks) c) Estimate the largest strain that can occur to any of the spring in the system. State which spring in your answer. Marks) (8 ka ka ks ma m2...
1. (50 pts) Consider the spin degree of freedom of an electron under an external magnetic field in the r-direction. The spin is initially (at time t 0) in the z-direction. (a) Write down the Hamiltonian for the electron spin. (Do you remember the elementary magnetic moment of electron, the Bohr magneton μΒ, in terms of electron mass me and the elementary charge e?) b) Write down the Schrödinger equation for the spin (c) Describe the motion of spin direction
1. Derive the equations of motion of the system shown in Fig 1 by using Lagrange's equations. Find the natural frequencies and mode shapes of the dynamical system for k 1 N/m, k-2 N/m, k I N/m, and mi 2 kg, m l kg, m -2 kg. scale the eigenvectors matrix Ф in order to achieve a mass normalized eigenvectors matrix Φ such that: F40 Fan Fig. 1
5. Consider the following time-dependent Lagrangian for a system with one degree of freedom , (10) where 8, m and k are fixed real constants greater than zero. (total 10 points) (a) Write down the Euler-Lagrange equation of motion for this system, and interpret the resulting equation in terms of a known physical system. (1 point) (b) Find Hamiltonian via Legendre transformation. (1 point) (c) Show that q(t) and the corresponding canonical momentum p(t) can be found as follows for...
For the system shown in Figure 6, a. How many degrees of freedom is this system and why? b. Write the equations of motion. For the remainder parts, assume alll the dampers are removed: c. If Ki=K3 and mim3, set the necessary matrix to find the natural frequencies and mode shapes d. For part c above, determine and explain how to get the natural frequencies. m1 Ty Absorber тз k1 С1 k3 m2 C2
For the system shown in Figure...
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