3. A mass weighing 2 pounds stretches a spring 1 foot. The mass is initially released...
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)...
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...
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...
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...
(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?
a mass weighing 8 pounds when attached to a spring, stretches it 6 inches.the object is originally at rest and is released 6 inches below equilibrium find the equation of motion if the surronding medium offers a damping force that is numerically equal to 5 times the instantaneous velocity
a mass weighing 8 pounds when attached to a spring, stretches it 6 inches.the object is originally at rest and is released 6 inches below equilibrium find the equation of motion if the surronding medium offers a damping force that is numerically equal to 5 times the instantaneous velocity
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.