A mass weighing 19lb stretches a spring 8in. The mass is attached to a viscous damper...

A mass weighing 19lb stretches a spring 8in. The mass is attached to a viscous damper with damping constant 4lb⋅s/ft. The mass is pushed upward, contracting the spring a distance of 2in, and then set into motion with a downward velocity of 7in/s. Determine the position u of the mass at any time t. Use 32ft/s2 as the acceleration due to gravity. Pay close attention to the units. Answer must be in inches

Expert Solution

Colby Messinger answered 5 days ago

A mass weighing 12lb stretches a spring 10in.. The mass is attached to a viscous damper...

A mass weighing 12lb stretches a spring 10in.. The mass is attached to a viscous damper with damping constant 3lb*s/ft. The mass is pushed upward, contracting the spring a distance of 2in, and then set into motion with a downward velocity of 4in/s. Determine the position of the mass at any time . Use as 32ft/s^2the acceleration due to gravity. Pay close attention to the units.

A mass weighing 12lb stretches a spring 10in. The mass is attached to a viscous damper...

A mass weighing 12lb stretches a spring 10in. The mass is attached to a viscous damper with damping constant 3lb⋅s/ft. The mass is pushed upward, contracting the spring a distance of 2in, and then set into motion with a downward velocity of 4in/s. Determine the position u of the mass at any time t. Use 32ft/s2 as the acceleration due to gravity. Pay close attention to the units. u(t)=

A mass weighing 17 lb stretches a spring 7 in. The mass is attached to a...

A mass weighing 17 lb stretches a spring 7 in. The mass is attached to a viscous damper with damping constant 2 lb *s/ft. The mass is pushed upward, contracting the spring a distance of 2 in, and then set into motion with a downward velocity of 2 in/s. Determine the position u of the mass at any time t. Use 32 ft/s^2 as the acceleration due to gravity. Pay close attention to the units. Leave answer in terms of...

A force of 400N stretches a spring 2m. A mass of 50kg is attached to the...

A force of 400N stretches a spring 2m. A mass of 50kg is attached to the end of the spring and put in a viscous fluid with a damping force that is 100 times the instantaneous velocity. The mass is released from the equilibrium position with a downward velocity of 1m/s. (a) Determine the natural frequency of the system. (b) Determine the level of damping in the system. (c) Write the differential equation of motion (d) Solve the system and...

A 8.50 kg mass is attached to the end of a hanging spring and stretches it...

A 8.50 kg mass is attached to the end of a hanging spring and stretches it 28.0 cm. It is then pulled down an additional 12.0 cm and then let go. What is the maximum acceleration of the mass? At what position does this occur? What is the position and velocity of the mass 0.63 s after release?

A mass weighing 10 pounds stretches a spring 3 inches. This mass is removed and replaces...

A mass weighing 10 pounds stretches a spring 3 inches. This mass is removed and replaces with a mass weighing 20 pounds, which is initially released from a point 4 inches above the equilibrium position with an upward velocity of 54 ft/s. Find the equation of motion, x(t) .

A mass of 20 grams stretches a spring 5cm. Suppose that the mass is also attached...

A mass of 20 grams stretches a spring 5cm. Suppose that the mass is also attached to a damper with constant coefficient 0.4 N·s/m. Initially the mass is pulled down an additional 2cm and released. Write a differential equation for the position u(t) of the mass at time t (make the units meters, kilograms, Newtons, seconds). Do NOT solve the differential equation. The solution to a differential equation that models a vibrating spring is u(t) = 4e−t cos(3t) + 3e−t...

A mass of 1 slug, when attached to a spring, stretches it 2 feet. It is...

A mass of 1 slug, when attached to a spring, stretches it 2 feet. It is released from a point 1 foot above the equilibrium position with a downward velocity of 2 ft/s. 1) Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 4 times the instantaneous velocity. 2) Classify the motion as underdamped, overdamped, or critically damped.

A mass of 1 slug, when attached to a spring, stretches it 2 feet and then...

A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting at t = 0, an external force equal to f(t) = 10 sin(4t) is applied to the system. Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity. (Use g = 32 ft/s2 for the acceleration due to gravity.) x(t) = ____________ft

A mass weighing 8 pounds stretches a spring 1 foot. The mass is initially released from...

A mass weighing 8 pounds stretches a spring 1 foot. The mass is initially released from rest from a point 2 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 2 times the instantaneous velocity. Find the equation of motion (solve the IVP) if the mass is driven by an external force equal to f(t) = 5 cos(2t). Graph the solution. What part of the...

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