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3. A mass weighing 4 pounds is suspended from a spring whose constant is 3 lb/ft. The entire syst...
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.
(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...
(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?
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...
3a. [10pts) A 32 lb weight is attached to a spring whose constant is 25 lb/ft....
3a. [10pts) A 32 lb weight is attached to a spring whose constant is 25 lb/ft. Initially the mass is released I ft below the equilibrium position with a downward velocity of 1 ft/sec. Find the equation of motion 3b. 10pts) Determine the equation of motion in part(a) if the surrounding medium offers a damping force numerically equal to 10 times the instantaneous velocity. 3c. [14pts) Determine the equation of motion in parts(a)-(b) if the weight is driven by an...
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...
Suppose a mass weighing 32 lb stretches a spring 2 ft. If the mass is released from rest at the e...
Suppose a mass weighing 32 lb stretches a spring 2 ft. If the mass is released from rest at the equilibrium position, find the equation of motion x(t) if an impressed force f (t) - sin t acts on the system for 0 t 2π and is then removed
Suppose a mass weighing 32 lb stretches a spring 2 ft. If the mass is released from rest at the equilibrium position, find the equation of motion x(t) if an impressed...
5. (20 points) A mass weighing 8 pounds stretches a spring 1.6 feet. The entire system...
5. (20 points) A mass weighing 8 pounds stretches a spring 1.6 feet. The entire system is placed in a medium that offers a damping force numerically equivalent to twice the instantaneous velocity. The mass is initially released from a point 1/2 foot above the equilibrium point with a downward velocity of 5 ft/sec. (a) (6 points) Write the differential equation for the mass/spring system and identify the initial conditions. 7 5. (b) (12 points) Solve the IVP in part...
A force of 2 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is...
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 numerically equal to 0.8 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) = Ae-At sin...
Suppose a mass weighing 32 lb stretches a spring 2 ft. If the mass is released from sin t acts on...
Suppose a mass weighing 32 lb stretches a spring 2 ft. If the mass is released from sin t acts on rest at the equilibrium position, find the equation of motion x(t) if an impressed force f(t) the system for 0 5 t < 2t and is then removed.
Suppose a mass weighing 32 lb stretches a spring 2 ft. If the mass is released from sin t acts on rest at 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...
(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?
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...
3a. [10pts) A 32 lb weight is attached to a spring whose constant is 25 lb/ft. Initially the mass is released I ft below the equilibrium position with a downward velocity of 1 ft/sec. Find the equation of motion 3b. 10pts) Determine the equation of motion in part(a) if the surrounding medium offers a damping force numerically equal to 10 times the instantaneous velocity. 3c. [14pts) Determine the equation of motion in parts(a)-(b) if the weight is driven by an...
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...
Suppose a mass weighing 32 lb stretches a spring 2 ft. If the mass is released from rest at the equilibrium position, find the equation of motion x(t) if an impressed force f (t) - sin t acts on the system for 0 t 2π and is then removed
Suppose a mass weighing 32 lb stretches a spring 2 ft. If the mass is released from rest at the equilibrium position, find the equation of motion x(t) if an impressed...
5. (20 points) A mass weighing 8 pounds stretches a spring 1.6 feet. The entire system is placed in a medium that offers a damping force numerically equivalent to twice the instantaneous velocity. The mass is initially released from a point 1/2 foot above the equilibrium point with a downward velocity of 5 ft/sec. (a) (6 points) Write the differential equation for the mass/spring system and identify the initial conditions. 7 5. (b) (12 points) Solve the IVP in part...
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 numerically equal to 0.8 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) = Ae-At sin...
Suppose a mass weighing 32 lb stretches a spring 2 ft. If the mass is released from sin t acts on rest at the equilibrium position, find the equation of motion x(t) if an impressed force f(t) the system for 0 5 t < 2t and is then removed.
Suppose a mass weighing 32 lb stretches a spring 2 ft. If the mass is released from sin t acts on rest at the equilibrium position, find the equation of motion...
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