a. Now the mass is pulled down 5 cm from rest and given an upward velocity of 10 cm/sec. Determine the IVP describing the motion of the mass b. Solve the resulting DE from part a Sketch the graph of the motion. d. Find the maximum displacement of the mass once it passes through the equilibrium
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A device is being designed that can be modeled as a mass-spring system. The mass-spring constant ...
The mass-spring constant is k = 10 g/sec2 and the damping coefficient is u= 20 g/sec....
The mass-spring constant is k = 10 g/sec2 and the damping coefficient is u= 20 g/sec. a. Now the mass is pulled down 5 cm from rest and given an upward velocity of 10 cm/sec. Determine the IVP describing the motion of the mass. b. Solve the resulting DE from part a. c. Sketch the graph of the motion. d. Find the maximum displacement of the mass once it passes through the equilibrium.
5. Use the same mass, damping coefficient, and spring constant as in #4. a. The mass...
5. Use the same mass, damping coefficient, and spring constant as in #4. a. The mass is pulled down 5 cm from rest and just released. Determine the IVP describing the motion of the mass. (6 pts) b. Solve the resulting DE from part a. (6 pts) c. Sketch the graph of the motion. (4 pts) 6 6.Again use the same mass, damping coefficient, and spring constant as in 4. a. Now the mass is pulled down 5 cm from...
A mass of 620 g stretches a spring 4 cm. If the spring-mass system is placed...
A mass of 620 g stretches a spring 4 cm. If the spring-mass system is placed in a medium that imparts a viscous force of 4 N when the speed of the mass is 9 cm/sec, find ?, the damping coefficient for this system. Use ?=9.8 m/sec2.
eN) For the spring-mass system shown, assume that m= 1 kg and k = 8m and the motion is fee Set up the 2" order ODE...
eN) For the spring-mass system shown, assume that m= 1 kg and k = 8m and the motion is fee Set up the 2" order ODE fot each situation 30 Point (e) The damping coefficient m/sec The damping coefficient is μ = 4 m/sec
eN) For the spring-mass system shown, assume that m= 1 kg and k = 8m and the motion is fee Set up the 2" order ODE fot each situation 30 Point (e) The damping coefficient m/sec...
A 5-kg mass is attached to a spring with stiffness 15 N/m. The damping constant for...
A 5-kg mass is attached to a spring with stiffness 15 N/m. The damping constant for the system is 10V3 N-sec/m. If the mass is pulled 10 cm to the right of equilibrium and given an initial rightward velocity of 2 m/sec, what is the maximum displacement from equilibrium that it will attain? The maximum displacement is meters. (Type an exact answer, using radicals as needed.)
4. (20 points) A mass pring system has a mass of kg, a damping constant of...
4. (20 points) A mass pring system has a mass of kg, a damping constant of kg/sec and a spring constant of 15 kg/sec2. There is no external force. The system is started in motion at y 4 meters with an initial velocity of 3 m/s in the downward direction. a) Find the differential equation and the initial conditions that describe the motion of this system. b) Solve the resulting initial value problem. c) Is the spring system overdamped, underdamped...
A 2 kg mass stretches a spring 1 meter. The mass is pushed upward, con- tracting...
A 2 kg mass stretches a spring 1 meter. The mass is pushed upward, con- tracting the spring a distance of 0.2 meters, and then set in motion with an upward velocity of 5 m/s. There is no damping. (a) Solve the IVP. You may use that the acceleration due to gravity is g = 10 m/s2 (b) What is the frequency of the motion? It is not necessary to specify units. (c) Sketch the phase portrait for this system....
A 4-kg mass is attached to a spring with stiffness 112 N/m. The damping constant for...
A 4-kg mass is attached to a spring with stiffness 112 N/m. The damping constant for the system is 16/7 N-sec/m. If the mass is pulled 20 cm to the right of equilibrium and given an initial rightward velocity of 2 m/sec, what is the maximum displacement from equilibrium that it will attain? 1 -2/7 617 1 (2+.4/7) 67 2+ meters. The maximum displacement is e (Type an exact answer, using radicals as needed.)
A 4-kg mass is attached to...
A 3-kg mass is attached to a spring with stiffness 81 N/m. The damping constant for...
A 3-kg mass is attached to a spring with stiffness 81 N/m. The damping constant for the system is 18/3 N-sec/m. If the mass is pulled 20 cm to the right of equilibrium and given an initial rightward velocity of 3 m/sec, what is the maximum displacement from equilibrium that it will attain? The maximum displacement is meters (Type an exact answer, using radicals as needed.)
1 point) A brick of mass 6 kg hangs from the end of a spring. When the brick is at rest, the spri...
Please solve both
1 point) A brick of mass 6 kg hangs from the end of a spring. When the brick is at rest, the spring is stretched by 3 cm. The spring is then stretched an additional 4 cm and eleased. Assume there is no air resistance. Note that the acceleration due to gravity-g, is g 980 cm/s Set up a differential equation with initial conditions describing the motion and solve it for the displacement s(t) of the mass...
5. Use the same mass, damping coefficient, and spring constant as in #4. a. The mass is pulled down 5 cm from rest and just released. Determine the IVP describing the motion of the mass. (6 pts) b. Solve the resulting DE from part a. (6 pts) c. Sketch the graph of the motion. (4 pts) 6 6.Again use the same mass, damping coefficient, and spring constant as in 4. a. Now the mass is pulled down 5 cm from...
eN) For the spring-mass system shown, assume that m= 1 kg and k = 8m and the motion is fee Set up the 2" order ODE fot each situation 30 Point (e) The damping coefficient m/sec The damping coefficient is μ = 4 m/sec
eN) For the spring-mass system shown, assume that m= 1 kg and k = 8m and the motion is fee Set up the 2" order ODE fot each situation 30 Point (e) The damping coefficient m/sec...
A 5-kg mass is attached to a spring with stiffness 15 N/m. The damping constant for the system is 10V3 N-sec/m. If the mass is pulled 10 cm to the right of equilibrium and given an initial rightward velocity of 2 m/sec, what is the maximum displacement from equilibrium that it will attain? The maximum displacement is meters. (Type an exact answer, using radicals as needed.)
4. (20 points) A mass pring system has a mass of kg, a damping constant of kg/sec and a spring constant of 15 kg/sec2. There is no external force. The system is started in motion at y 4 meters with an initial velocity of 3 m/s in the downward direction. a) Find the differential equation and the initial conditions that describe the motion of this system. b) Solve the resulting initial value problem. c) Is the spring system overdamped, underdamped...
A 2 kg mass stretches a spring 1 meter. The mass is pushed upward, con- tracting the spring a distance of 0.2 meters, and then set in motion with an upward velocity of 5 m/s. There is no damping. (a) Solve the IVP. You may use that the acceleration due to gravity is g = 10 m/s2 (b) What is the frequency of the motion? It is not necessary to specify units. (c) Sketch the phase portrait for this system....
A 4-kg mass is attached to a spring with stiffness 112 N/m. The damping constant for the system is 16/7 N-sec/m. If the mass is pulled 20 cm to the right of equilibrium and given an initial rightward velocity of 2 m/sec, what is the maximum displacement from equilibrium that it will attain? 1 -2/7 617 1 (2+.4/7) 67 2+ meters. The maximum displacement is e (Type an exact answer, using radicals as needed.)
A 4-kg mass is attached to...
A 3-kg mass is attached to a spring with stiffness 81 N/m. The damping constant for the system is 18/3 N-sec/m. If the mass is pulled 20 cm to the right of equilibrium and given an initial rightward velocity of 3 m/sec, what is the maximum displacement from equilibrium that it will attain? The maximum displacement is meters (Type an exact answer, using radicals as needed.)
Please solve both
1 point) A brick of mass 6 kg hangs from the end of a spring. When the brick is at rest, the spring is stretched by 3 cm. The spring is then stretched an additional 4 cm and eleased. Assume there is no air resistance. Note that the acceleration due to gravity-g, is g 980 cm/s Set up a differential equation with initial conditions describing the motion and solve it for the displacement s(t) of the mass...
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