QUESTION 1 Which two things does a mechanical system have to have in order to exhibit...
QUESTION 1 Which two things does a mechanical system have to have in order to exhibit oscillatory behavior? a. Inertia and a restoring force b. Inertia and gravity c. An equilibrium position and a restoring force d. Gravity and potential energy
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QUESTION 1 Which two things does a mechanical system have to
have in order to exhibit...
Hooke's Law represents a linear restoring force where an elastic system is displaced from equilibrium. In...
Hooke's Law represents a linear restoring force where an elastic system is displaced from equilibrium. In an experiment a rubber band and a spring were placed in a vertical position and a series of having Masses were attached to the free end. a) Does the rubber band used exhibit Hooke's Law behavior? Why or why not? b) Does the spring used exhibit Hooke's Law behavior ? Why or why not? c) Simple Harmonic Motion is oscillatory motion of a system...
Problem 3: For the mechanical system shown below, perform the following tasks: 1) Develop second-order differential equ...
Problem 3: For the mechanical system shown below, perform the following tasks: 1) Develop second-order differential equations of motion for the position of the two hinged bars assuming small angles of motion and using angular rotation of bars 1 and 2 as the output variables, 2) write the equations of motion in state-space form, 3) state the output vector for force in spring k2. Note: Gravity acts downward with acceleration 'g O2 dz m2, L2 my L d3 www.jwwww B...
Question 16 3.5 pts Students attach a thin strip of metal to a table so that...
Question 16 3.5 pts Students attach a thin strip of metal to a table so that the strip is horizontal in relation to the ground. A section of the strip hangs off the edge of the table. A mass is secured to the end of the hanging section of the strip and is then displaced so that the mass-strip system oscillates, as shown in the figure. Students make various measurements of the net force F exerted on the mass as...
Question 3 (35 marks) Consider a mechanical system shown in Figure 3. The system is at rest for t
Question 3 (35 marks) Consider a mechanical system shown in Figure 3. The system is at rest for t<0. The input force f is applied at 0. The displacement x is the output of the system and is measured from the equilibrium position. kI b2 bi it Figure 3. Schematic of a mechanical system. (a) Obtain the traf) (10 marks) X (s) F(s) (b) Use of force-voltage analogy, obtain the equations for an electrical system (5 marks) (c) Draw a...
2. (15 scores) Consider the mechanical system shown in Figure 1. A spring exerts a force...
2. (15 scores) Consider the mechanical system shown in Figure 1. A spring exerts a force that is a function of its extension. A damper exerts a force that is a function of the velocity of the piston. Assume that the spring and the damper are both linear. (1) We want to describe the relation between the external force F(t) and the position yt) of the mass. Give the differential equation relating F(t) and y(t). Define this carefully as a...
1) Which function is NOT a p Populations of organis B) Living things exhibit co C)...
1) Which function is NOT a p Populations of organis B) Living things exhibit co C) Organisms take in energy unction is NOT a property of life? hs of organisms rarely change over time. Wings exhibit complex but ordered organization. ake in energy and use it to perform all of life's activities. Organisms reproduce their own kind. 2) What are the two main p A) speciation and evolution C) decomposition and nutrient recycling the two main processes upon which ecosystems...
Question 2 (40 marks) A micro-electrical-mechanical system consists of two members as shown below...
Finite element method
Question 2 (40 marks) A micro-electrical-mechanical system consists of two members as shown below. It is important that the displacement of the slider is accurately known for a given force, F. To find the relation between displacement and F, it was decided to use FE method. Node 1 is fully constrained, node 2 is free to rotate and translate along the horizontal, and node 3 is only free to rotate. (a) Select the appropriate element types for...
A horizontal block-spring system with the block on a frictionless surface has total mechanical energy E...
A horizontal block-spring system with the block on a frictionless surface has total mechanical energy E = 53.7 ) and a maximum displacement from equilibrium of 0.200 m. (a) What is the spring constant? N/m (b) What is the kinetic energy of the system at the equilibrium point? (c) If the maximum speed of the block is 3.45 m/s, what is its mass? | kg (d) What is the speed of the block when its displacement is 0.160 m? m/s...
5. Consider the system: dz 4y 1 dy (a) Are these species predator-prey or competing? b) What type of growth does species z exhibit in absence of species y? What type of growth does species y exhibit...
5. Consider the system: dz 4y 1 dy (a) Are these species predator-prey or competing? b) What type of growth does species z exhibit in absence of species y? What type of growth does species y exhibit in absence of species r? (c) Find all critical (equilibrium) points d) Using the Jacobian matrix, classify (if possible) each critical (equilibrium) point as a stable node, a stable spiral point, an unstable node, an unstable spiral point, or a saddle point. (e)...
1. Consider a system of two Einstein solids, A and B, each containing 4 oscillators, sharing...
1. Consider a system of two Einstein solids, A and B, each containing 4 oscillators, sharing a total of 4 units of energy. Assume that the solids are weakly coupled, and that the total energy is fixed. a. How many different macrostates are available to this system? b. How many different microstates are available to this system? c. Assuming that this system is in thermal equilibrium, what is the probability of finding all the energy in solid A? d. What...
Problem 3: For the mechanical system shown below, perform the following tasks: 1) Develop second-order differential equations of motion for the position of the two hinged bars assuming small angles of motion and using angular rotation of bars 1 and 2 as the output variables, 2) write the equations of motion in state-space form, 3) state the output vector for force in spring k2. Note: Gravity acts downward with acceleration 'g O2 dz m2, L2 my L d3 www.jwwww B...
Question 16 3.5 pts Students attach a thin strip of metal to a table so that the strip is horizontal in relation to the ground. A section of the strip hangs off the edge of the table. A mass is secured to the end of the hanging section of the strip and is then displaced so that the mass-strip system oscillates, as shown in the figure. Students make various measurements of the net force F exerted on the mass as...
Question 3 (35 marks) Consider a mechanical system shown in Figure 3. The system is at rest for t<0. The input force f is applied at 0. The displacement x is the output of the system and is measured from the equilibrium position. kI b2 bi it Figure 3. Schematic of a mechanical system. (a) Obtain the traf) (10 marks) X (s) F(s) (b) Use of force-voltage analogy, obtain the equations for an electrical system (5 marks) (c) Draw a...
2. (15 scores) Consider the mechanical system shown in Figure 1. A spring exerts a force that is a function of its extension. A damper exerts a force that is a function of the velocity of the piston. Assume that the spring and the damper are both linear. (1) We want to describe the relation between the external force F(t) and the position yt) of the mass. Give the differential equation relating F(t) and y(t). Define this carefully as a...
1) Which function is NOT a p Populations of organis B) Living things exhibit co C) Organisms take in energy unction is NOT a property of life? hs of organisms rarely change over time. Wings exhibit complex but ordered organization. ake in energy and use it to perform all of life's activities. Organisms reproduce their own kind. 2) What are the two main p A) speciation and evolution C) decomposition and nutrient recycling the two main processes upon which ecosystems...
Finite element method
Question 2 (40 marks) A micro-electrical-mechanical system consists of two members as shown below. It is important that the displacement of the slider is accurately known for a given force, F. To find the relation between displacement and F, it was decided to use FE method. Node 1 is fully constrained, node 2 is free to rotate and translate along the horizontal, and node 3 is only free to rotate. (a) Select the appropriate element types for...
A horizontal block-spring system with the block on a frictionless surface has total mechanical energy E = 53.7 ) and a maximum displacement from equilibrium of 0.200 m. (a) What is the spring constant? N/m (b) What is the kinetic energy of the system at the equilibrium point? (c) If the maximum speed of the block is 3.45 m/s, what is its mass? | kg (d) What is the speed of the block when its displacement is 0.160 m? m/s...
5. Consider the system: dz 4y 1 dy (a) Are these species predator-prey or competing? b) What type of growth does species z exhibit in absence of species y? What type of growth does species y exhibit in absence of species r? (c) Find all critical (equilibrium) points d) Using the Jacobian matrix, classify (if possible) each critical (equilibrium) point as a stable node, a stable spiral point, an unstable node, an unstable spiral point, or a saddle point. (e)...
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