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2. A mass weighing 4 pounds is attached to a spring whose spring constant is 2...
A mass weighing 4 pounds is attached to a spring whase constant is 2 b/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released fr...
A mass weighing 4 pounds is attached to a spring whase constant is 2 b/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilbrium position with a downward velocity of 10 ft/s. Determine the time at which the mass passes through the equilibrium position. (Use g 32 ft/s2 for the acceleration due to gravity.) Find the time after the mass passes through...
A mass weighing 4 pounds is attached to a spring whose constant is 2 lb/ft
A mass weighing 4 pounds is attached to a spring whose constant is 2 lb/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 16 ft/s. (g = 32 ft/s2) a. Find the equation of motion. b. What type of motion is this? c. Determine the time at which the mass passes through the equilibrium position.
A 4 foot spring measures 8 feet long after a mass weighing 8 pounds is attached...
A 4 foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to 2^1/2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 9 ft/a. (Use g =32 ft/s^2 for the acceleration due to gravity.) a) Find the time at which the mass attains its extreme...
A mass weighing 8 pounds stretches a spring 1 foot. The system is then immersed in...
A mass weighing 8 pounds stretches a spring 1 foot. The system is then immersed in a medium that offers a damping force numerically equal to 3 times the instantaneous velocity. The mass is initially released from the equilibrium position with a downward velocity of 4 ft/s. Find the spring constant ?, mass ? and the damping constant ? Find ? and ?, and the roots of the characteristic equation: Write the initial conditions: Estimate the time when the mass...
2. (24 pts) A 4-foot spring measures 6 feet long after a mass weighing 8 pounds...
2. (24 pts) A 4-foot spring measures 6 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to 1.5 times the instantaneous velocity. If the mass is initially released from the equilibrium position with a downward velocity of 7 ft/s. (Use g = 32 ft/s2 for the acceleration due to gravity.) (a) (8 pts) Find the equation of motion. (b) (6 pts) Find the...
3. A mass weighing 4 pounds is suspended from a spring whose constant is 3 lb/ft. The entire syst...
3. A mass weighing 4 pounds is suspended from a spring whose constant is 3 lb/ft. The entire system is emersed in a fluid offering a damping force numerically equal to the instantaneous velocity. The mass is initially released from rest at a point 2 feet below the equilibrium position. An external force equal to f(t) = e-t is impressed on the system. Find the steady-state solution.
3. A mass weighing 4 pounds is suspended from a spring whose constant...
(7 points) 14. A mass weighing 4 pounds stretches a spring 2 feet. The system is...
(7 points) 14. A mass weighing 4 pounds stretches a spring 2 feet. The system is submerged in a medium which offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 8 ft/s. Find the equation of motion, ä(t). What type of damped motion is this system?
5. (16) A box weighing 16 pounds is attached to a spring with spring constant 8...
5. (16) A box weighing 16 pounds is attached to a spring with spring constant 8 lb/ft. The box is initially released from a point 2 foot above the equilibrium position with an upward velocity of 3 ft/sec. (a) Set up the DE for this system. Do not solve the DE. Show your work. Write the equation in standard form. Write your answer in the box (b) Convert the initial conditions into mathematical equations. (0) '(0) = (c) Now suppose...
5. (16) A box weighing 16 pounds is attached to a spring with spring constant 8...
5. (16) A box weighing 16 pounds is attached to a spring with spring constant 8 1b/ft. The book is initially released from a point 2 foot above the equilibrium position with an upward velocity of 3 ft/sec (a) Set up the DE for this system. Do not solve the DE. Show your work. Write the equation in standard form. Write your answer in the box NIP 32 -IN .+ 8x=0 • levo (b) Convert the initial conditions into mathematical...
(7 points) 13. A mass weighing 10 pounds stretches a spring 3 inches. The mass is...
(7 points) 13. A mass weighing 10 pounds stretches a spring 3 inches. The mass is removed and replaced with a mass weighing 51.2 pounds, which is initially released from a point 4 inches above the equilibrium position with an downward velocity of ft/s. Find the equation of motion, ä(t). (g = 32 ft/s2) (7 points) 14. A mass weighing 4 pounds stretches a spring 2 feet. The system is submerged in a medium which offers a damping force that...
A mass weighing 4 pounds is attached to a spring whase constant is 2 b/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilbrium position with a downward velocity of 10 ft/s. Determine the time at which the mass passes through the equilibrium position. (Use g 32 ft/s2 for the acceleration due to gravity.) Find the time after the mass passes through...
2. (24 pts) A 4-foot spring measures 6 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to 1.5 times the instantaneous velocity. If the mass is initially released from the equilibrium position with a downward velocity of 7 ft/s. (Use g = 32 ft/s2 for the acceleration due to gravity.) (a) (8 pts) Find the equation of motion. (b) (6 pts) Find the...
3. A mass weighing 4 pounds is suspended from a spring whose constant is 3 lb/ft. The entire system is emersed in a fluid offering a damping force numerically equal to the instantaneous velocity. The mass is initially released from rest at a point 2 feet below the equilibrium position. An external force equal to f(t) = e-t is impressed on the system. Find the steady-state solution.
3. A mass weighing 4 pounds is suspended from a spring whose constant...
(7 points) 14. A mass weighing 4 pounds stretches a spring 2 feet. The system is submerged in a medium which offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 8 ft/s. Find the equation of motion, ä(t). What type of damped motion is this system?
5. (16) A box weighing 16 pounds is attached to a spring with spring constant 8 lb/ft. The box is initially released from a point 2 foot above the equilibrium position with an upward velocity of 3 ft/sec. (a) Set up the DE for this system. Do not solve the DE. Show your work. Write the equation in standard form. Write your answer in the box (b) Convert the initial conditions into mathematical equations. (0) '(0) = (c) Now suppose...
5. (16) A box weighing 16 pounds is attached to a spring with spring constant 8 1b/ft. The book is initially released from a point 2 foot above the equilibrium position with an upward velocity of 3 ft/sec (a) Set up the DE for this system. Do not solve the DE. Show your work. Write the equation in standard form. Write your answer in the box NIP 32 -IN .+ 8x=0 • levo (b) Convert the initial conditions into mathematical...
(7 points) 13. A mass weighing 10 pounds stretches a spring 3 inches. The mass is removed and replaced with a mass weighing 51.2 pounds, which is initially released from a point 4 inches above the equilibrium position with an downward velocity of ft/s. Find the equation of motion, ä(t). (g = 32 ft/s2) (7 points) 14. A mass weighing 4 pounds stretches a spring 2 feet. The system is submerged in a medium which offers a damping force that...
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