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Classical Mechanics problem:
Consider the two coupled pendulums shown in the figure below. Each of the...
A2. Two identical simple pendulums are connected via a spring as it is shown in Figure A2. The length of the pendulum strut L-0.5m and the mass of attached bob m-2kg, the stiffness coefficient of the...
A2. Two identical simple pendulums are connected via a spring as it is shown in Figure A2. The length of the pendulum strut L-0.5m and the mass of attached bob m-2kg, the stiffness coefficient of the connecting spring is k-80Ns/m. 02 Figure A2. a) Using the free-body diagram method derive the following governing equations for the coupled pendulum system which are given below in matrix form b) Using the characteristic equation method or transformation to principal coordinates find out two...
Week Seven Coursework 1 Classical Mechanics The figure shows a compound pendulum. A mass 3m is...
Week Seven Coursework 1 Classical Mechanics The figure shows a compound pendulum. A mass 3m is suspended from a fixed point, by a light, inextensible string of length L. A second mass m is suspended from the first by an identical string 1.1. For the system in its equilibrium position, as shown in the left-hand image, write down the tension in the two strings. [4 marks) 1.2. For small displacements, we may assume the tension in each string remains the...
Question 2: Coupled Systems with Friction Consider a system with two DoFs such that the Lagrangia...
Question 2: Coupled Systems with Friction Consider a system with two DoFs such that the Lagrangian is: 2 2 2 2 2 Now we add universal friction to the system, that is, for each of the E-L equation we add a term aivi. 1. In the 0 limit, find the eigenmodes and eignevalues of the system 2. In general, once we add friction, the system cannot be separated into normal modes However, there are specific values of ai that allow...
Frictionless plane M 1.) Consider the coupled system shown at the right. The mass M is...
Frictionless plane M 1.) Consider the coupled system shown at the right. The mass M is free to slide on a frictionless surface and is connected to the wall with a spring of spring constant k. Mass M2 is 2000 attached to My with taut rope of length (it acts as a pendulum). The vertical line shows the equilibrium position when the spring is un- stretched (r = 0). The coordinates 21 and 12 denote the positions of the two...
I. COUPLED OSCILLATIONS Consider the system below with two degrees of freedom (neglect gravitation). Denote the...
I. COUPLED OSCILLATIONS Consider the system below with two degrees of freedom (neglect gravitation). Denote the displacement of each of the particles with respect to equilibrium by óy (t), i= 1,2. 1. Find the Lagrangian describing the system 2. Write down the coupled equations of motion for óyn (t) and by2(t) 3. Find the 2 x 2 matrices Ť and V and solve the normal mode equation for w: det(V-2T) 0. 4. Compute the form of the eigenvectors (normal modes),...
IV. Spring-Mass System Application - Consider the system of two masses and three springs as shown...
IV. Spring-Mass System Application - Consider the system of two masses and three springs as shown in the figure below. Let z(t) be the position mass m, and y(t) be the position of mass m. Let m, = 1, m, = 1, k, = 4, k, = 6, and k, = 4. ksi-ik, a.) Model the system with two second order differential equations. 6a.) System: b) Find the general solution to the system using the constants.) head of your choice....
1. Note: Drawings are not to scale.) You are given two objects, each with the same...
1. Note: Drawings are not to scale.) You are given two objects, each with the same mass. One object is a solid, uniform disk of outer radius R The other object is a thin, uniform rod of unknown length Initially these objects are suspended as shown (each from a frictionless pin located on its uppermost edge). When allowed to oscillate freely as pendulums (through small angular displacements), they have equal frequencies. disk rod Then the rod is removed from its...
Problem 7: Consider the two-degrees of freedom system shown in the figure below, where each disk...
Problem 7: Consider the two-degrees of freedom system shown in the figure below, where each disk is pivoted at its mass center. The inputs are the torques τι and T2 applied to the pivot points. At t = 0, θί-B2 = τι-T2-0, and each linear spring is at its free length (undeformed). Find the equivalent inertia (la) and stiffness (K matrix T1 T2 02 J2, r2
please answer all prelab questions, 1-4. This is the prelab manual, just in case you need...
please answer all prelab questions, 1-4.
This is the prelab manual, just in case you need background
information to answer the questions. The prelab questions are in
the 3rd photo.
this where we put in the answers, just to give you an
idea.
Lab Manual Lab 9: Simple Harmonic Oscillation Before the lab, read the theory in Sections 1-3 and answer questions on Pre-lab Submit your Pre-lab at the beginning of the lab. During the lab, read Section 4 and...
A2. Two identical simple pendulums are connected via a spring as it is shown in Figure A2. The length of the pendulum strut L-0.5m and the mass of attached bob m-2kg, the stiffness coefficient of the connecting spring is k-80Ns/m. 02 Figure A2. a) Using the free-body diagram method derive the following governing equations for the coupled pendulum system which are given below in matrix form b) Using the characteristic equation method or transformation to principal coordinates find out two...
Week Seven Coursework 1 Classical Mechanics The figure shows a compound pendulum. A mass 3m is suspended from a fixed point, by a light, inextensible string of length L. A second mass m is suspended from the first by an identical string 1.1. For the system in its equilibrium position, as shown in the left-hand image, write down the tension in the two strings. [4 marks) 1.2. For small displacements, we may assume the tension in each string remains the...
Question 2: Coupled Systems with Friction Consider a system with two DoFs such that the Lagrangian is: 2 2 2 2 2 Now we add universal friction to the system, that is, for each of the E-L equation we add a term aivi. 1. In the 0 limit, find the eigenmodes and eignevalues of the system 2. In general, once we add friction, the system cannot be separated into normal modes However, there are specific values of ai that allow...
Frictionless plane M 1.) Consider the coupled system shown at the right. The mass M is free to slide on a frictionless surface and is connected to the wall with a spring of spring constant k. Mass M2 is 2000 attached to My with taut rope of length (it acts as a pendulum). The vertical line shows the equilibrium position when the spring is un- stretched (r = 0). The coordinates 21 and 12 denote the positions of the two...
I. COUPLED OSCILLATIONS Consider the system below with two degrees of freedom (neglect gravitation). Denote the displacement of each of the particles with respect to equilibrium by óy (t), i= 1,2. 1. Find the Lagrangian describing the system 2. Write down the coupled equations of motion for óyn (t) and by2(t) 3. Find the 2 x 2 matrices Ť and V and solve the normal mode equation for w: det(V-2T) 0. 4. Compute the form of the eigenvectors (normal modes),...
IV. Spring-Mass System Application - Consider the system of two masses and three springs as shown in the figure below. Let z(t) be the position mass m, and y(t) be the position of mass m. Let m, = 1, m, = 1, k, = 4, k, = 6, and k, = 4. ksi-ik, a.) Model the system with two second order differential equations. 6a.) System: b) Find the general solution to the system using the constants.) head of your choice....
1. Note: Drawings are not to scale.) You are given two objects, each with the same mass. One object is a solid, uniform disk of outer radius R The other object is a thin, uniform rod of unknown length Initially these objects are suspended as shown (each from a frictionless pin located on its uppermost edge). When allowed to oscillate freely as pendulums (through small angular displacements), they have equal frequencies. disk rod Then the rod is removed from its...
Problem 7: Consider the two-degrees of freedom system shown in the figure below, where each disk is pivoted at its mass center. The inputs are the torques τι and T2 applied to the pivot points. At t = 0, θί-B2 = τι-T2-0, and each linear spring is at its free length (undeformed). Find the equivalent inertia (la) and stiffness (K matrix T1 T2 02 J2, r2
please answer all prelab questions, 1-4.
This is the prelab manual, just in case you need background
information to answer the questions. The prelab questions are in
the 3rd photo.
this where we put in the answers, just to give you an
idea.
Lab Manual Lab 9: Simple Harmonic Oscillation Before the lab, read the theory in Sections 1-3 and answer questions on Pre-lab Submit your Pre-lab at the beginning of the lab. During the lab, read Section 4 and...
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