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A 288-kg mass, when attached to the end of a spring hanging vertically, stretches the spring...
A 189-kg mass, when attached to the end of a spring hanging vertically, stretches the spring 9 m. The mass is in a medium that exerts a viscous resistance of 3024 N when the mass has a velocity of 4 m/sec. Assume the mass is given an initial velocity of 14 m/s from the equilibrium position. a) Determine the spring constant k. Use g = 10 m/sec. k b) Determine the damping coeffient 7. 7 c) If the initial value...
A mass of 2 kg stretches a spring 0.1 m. At time t= 0 the mass is released from its equilibrium position with a downward velocity of 1 m/s. Air resistance adds a damping force equal to one fifth of the velocity of the mass. Set up an initial value problem for the position x(t) of the mass at time t. Determine whether the system is overdamped, underdamped or critically damped. You can assume the acceleration of gravity g equals...
1) A force of 2 N stretches a spring 0.5 meters. The mass of 1 kg is attached to the spring and set into motion in a medium that offer a damped force equal 4 times the velocity. If the mass is at stating from 0.5 m above the equilibrium position with a downward initial velocity of 0.2m/sec a) Find the equation for the position if the system is exerted by an external force of f(t) = 4 cost. b)...
A mass weighing 52lb stretches a spring 7.5in. The mass is also attached to a damper with coeffient Y. Determine the value of Y for which the system is critically damped. Assume that g=32ft/s^2
A 2 kg mass is hung from a spring and stretches it 12 cm. The mass is also attached to a viscous damper that exerts a force of 3 N when the velocity of the mass is 4 m/s. The mass is pulled down 7 cm below its equilibrium position and given an initial downward velocity of 10 cm/s. Find an initial value problem that models the displacement of the mass, measured in meters, from the equilibrium position.
(1 point) A mass weighing 8 lb stretches a spring 3 in. Suppose the mass is displaced an additional 11 in in the positive (downward) direction and then released with an initial upward velocity of 2 ft/s. The mass is in a medium, that exerts a viscuouse resistance of 1 lb when the mass has a velocity of 4 ft/s. Assume g 32 ft/s is the gravitational acceleration (a) Find the mass m (in lb.s/ft) (b) Find the damping coefficient...
helpful formulas: mu’’(t)+cu’(t)+ku(t)=0 m is the mass c is the damping coefficiant k is spring constant Fd=cu’(t) k=mg/(spring displacement) A mass of 1.5 kg stretches a spring 0.08 m. The mass is in a medium that exerts a viscous resistance of 25 N when the mass has a velocity of 2 m. The viscous resistance is proportional to the speed of the object. Suppose the object is displaced an additional 0.03 m and released. Find an function to express the...
A 10 kg mass attached to a spring stretches the spring 2 m beyond its natural length. At time t = 0, an external force of f (t ) = 20cos 4t Newtons is applied to the system, and the system is damped by a force of 3 N per m/s of motion. Assuming an initial position at equilibrium and no initial velocity, find the equation of motion and the phase angle. You can use decimals here if you hate...
differential equations: a mass of 2kg stretches a spring 1m. the mass is in a medium that exerts a viscous resistance of 8 newtons when the velocity of the mass is 2m/sec. the mass is stretched from its equilibrium position 1m and then set in motion with a downward velocity of (3sqrt(3) - 1) m/sec. Let g=10 m/sec^2 a)state and solve the initial value problem for u(t), the displacement of the mass from its equilibrium position b) what is the...
A mass of m kilograams (kg) is mounted on top of a vertical spring. The spring is L metres long when disengaged and the end not attached to the mass is fixced to the ground. The mass moves vertically up and down, acted on by gravity, the restoring force T of the spring and the damping force R due to friction: see the diagram below The gravitational force is mg dowswards, where g- 9.8m is acceleration due to gravity, measured...