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Problems 1 and 2
A mass weighing 3/4 slug, attached to the end of a spring...
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.
1. A force of 2 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds...
1. A force of 2 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force that is equal to 0.4 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. (Use the convention that displacements measured below the equilibrium position are positive.) (b)...
2. A mass weighing 4 pounds is attached to a spring whose spring constant is 2...
2. A mass weighing 4 pounds is attached to a spring whose spring constant is 2 Ib/ft. The system is subjected to 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. (a) Establish the initial-value problem which governs this motion. (b) Solve this initial-value problem. (c) Find the time at which the mass attains its extreme displacement...
Use Laplace's method to solve A mass of 1 slug is attached to a spring whose...
Use Laplace's method to solve A mass of 1 slug is attached to a spring whose constant is 5 lb/ft. Initially, the mass is released 1 foot below the equilibrium position with a downward velocity of 3 ft/s, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 2 times the instantaneous velocity. (a) Find the equation of motion if the mass is driven by an external force equal to f(t)...
In problems 14-17, set up the spring mass equation. Determine whether it is undamped, under, critically...
In problems 14-17, set up the spring mass equation. Determine whether it is undamped, under, critically or overdamped. Solve the IVP and draw a graph (technology is cool) of the solution on the interval 0 < t < 12. If the system Is underdamped convert the solution to the form Re^alpha t sin(beta t + delta) A mass weighing 64 pounds stretches a spring 0.32 foot. The mass is initially released from a point 8 inches above the equilibrium position...
4. (15 pts) A mass weighing 8 pounds, attached to the end of a spring, stretches...
4. (15 pts) A mass weighing 8 pounds, attached to the end of a spring, stretches it 6 inches. Initially, the mass is released from a point 2 inches above the equilibrium position. Find the equation of motion.
(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...
1. A mass weighing 8 pounds is attached to a 4 foot long spring and stretches it to 8 feet long. ...
1. A mass weighing 8 pounds is attached to a 4 foot long spring and stretches it to 8 feet long. The medium offers a damping force equal to 0.5 times the instantaneous velocity. Find the equation of motion if the mass is released from rest at a position 18 inches above the equilibrium.
1. A mass weighing 8 pounds is attached to a 4 foot long spring and stretches it to 8 feet long. The medium offers a damping...
A force of 4 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is...
A force of 4 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 0.4 times the instantaneous velocity (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. x(t) = ft (b) Express the equation of motion in the form x(t) = Aet...
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...
1. A force of 2 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force that is equal to 0.4 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. (Use the convention that displacements measured below the equilibrium position are positive.) (b)...
2. A mass weighing 4 pounds is attached to a spring whose spring constant is 2 Ib/ft. The system is subjected to 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. (a) Establish the initial-value problem which governs this motion. (b) Solve this initial-value problem. (c) Find the time at which the mass attains its extreme displacement...
In problems 14-17, set up the spring mass equation. Determine whether it is undamped, under, critically or overdamped. Solve the IVP and draw a graph (technology is cool) of the solution on the interval 0 < t < 12. If the system Is underdamped convert the solution to the form Re^alpha t sin(beta t + delta) A mass weighing 64 pounds stretches a spring 0.32 foot. The mass is initially released from a point 8 inches above the equilibrium position...
4. (15 pts) A mass weighing 8 pounds, attached to the end of a spring, stretches it 6 inches. Initially, the mass is released from a point 2 inches above the equilibrium position. Find the equation of motion.
(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...
1. A mass weighing 8 pounds is attached to a 4 foot long spring and stretches it to 8 feet long. The medium offers a damping force equal to 0.5 times the instantaneous velocity. Find the equation of motion if the mass is released from rest at a position 18 inches above the equilibrium.
1. A mass weighing 8 pounds is attached to a 4 foot long spring and stretches it to 8 feet long. The medium offers a damping...
A force of 4 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 0.4 times the instantaneous velocity (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. x(t) = ft (b) Express the equation of motion in the form x(t) = Aet...
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...
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