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. (25 points) A mass weighing 2 lb stretches a spring 6 in. If the mass is pulled down an additional 3 in. and then released, and if there is no damping, determine the position u of the mass at a...
A mass weighing 9 lb stretches a spring 8 in. The mass is pulled down an...
A mass weighing 9 lb stretches a spring 8 in. The mass is pulled down an additional 7 in and is then set in motion with an initial upward velocity of 2 ft/s. No damping is applied. a. Determine the position u of the mass at any time t. Use 32 ft/s as the acceleration due to gravity. Pay close attention to the units. u(t) = 5 cos (4 3 t) + sin(4V3 t) 2V3 b. Determine the period, amplitude...
3. < Previous Ne A mass weighing 9 lb stretches a spring 4 in. The mass...
3. < Previous Ne A mass weighing 9 lb stretches a spring 4 in. The mass is pulled down an additional 3 in and is then set in motion with an initial upward velocity of 6 ft/s. No damping is applied. a. Determine the position u of the mass at any time t. Use 32 ft/s as the acceleration due to gravity. Pay close attention to the units. u(t) = ft b. Determine the period, amplitude and phase of the...
A mass weighing 16 lb stretches a spring 3 in. the mass is attached to a viscous damper with a da...
A mass weighing 16 lb stretches a spring 3 in. the mass is attached to a viscous damper with a damping constant of 2 lb s/ft. if the mass is set in motion from its equilibrium position with a downward velocity of 3 in/s. (1) find its position u(t) at any time t. Plot u versus t. (2) Determine the quasi frequency and the quasi period. (3) find the time τ such that |u(t)| < 0.01 in for all t...
A mass weighing 11 lb stretches a spring 8 in. The mass is attached to a...
A mass weighing 11 lb stretches a spring 8 in. The mass is attached to a viscous damper with damping constant 3 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 6 in/s. Determine the position u of the mass at any time t. Use 32 ft/s as the acceleration due to gravity. Pay close attention to the units. u(t) =
< Pre A mass weighing 18 lb stretches a spring 6 in. The mass is attached...
< Pre A mass weighing 18 lb stretches a spring 6 in. 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 4 in, and then set into motion with a downward velocity of 5 in/s. Determine the position u of the mass at any time t. Use 32 ft/s” as the acceleration due to gravity. Pay close attention to the units. u(t) = in
A mass weighing 10 lb stretches a spring 11 in. The mass is attached to a...
A mass weighing 10 lb stretches a spring 11 in. The mass is attached to a viscous damper with damping constant 3 lb ·s/ft. The mass is pushed upward, contracting the spring a distance of 4 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 as the acceleration due to gravity. Pay close attention to the units. u(t) =
A mass weighting 3 lb stretches a spring 3 in. if the mass is pushed upward,...
A mass weighting 3 lb stretches a spring 3 in. if the mass is pushed upward, contracting the spring a distance of 1 in, and then set in motion with a downward velocity of 2 ft/s, and if there is no damping. (1) determine the position u(t) of the mass at any time t. (2) Determine the frequency, period, amplitude, and phase of the motion. (3) Plot u(t), and find when does the mass first return to its equilibrium position?...
A mass weighing 4 pounds stretches a spring 6 inches. At time t = 0, the...
A mass weighing 4 pounds stretches a spring 6 inches. At time t = 0, the weight is then struck to set it into motion with an initial velocity of 2 ft/sec, directed downward. Determine the equations of motion for the position and the velocity of the weight. Find the amplitude, period, and frequency of the position (displacement). A 4-lb weight stretches a spring 1 ft. If the weight moves in a medium where the magnitude of the damping force...
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...
A mass of 2 kg stretches a spring 40 cm. The mass is pulled downward 1m...
A mass of 2 kg stretches a spring 40 cm. The mass is pulled downward 1m and released with an upwards velocity of 2m/s. Assuming there is no damping and that^1 the acceleration due to gravity is g = 10m/s^2, determine the position u(t) of the mass at time t, as well as the amplitude, period, frequency, and phase. Provide a rough sketch of the graph of the solution.
A mass weighing 9 lb stretches a spring 8 in. The mass is pulled down an additional 7 in and is then set in motion with an initial upward velocity of 2 ft/s. No damping is applied. a. Determine the position u of the mass at any time t. Use 32 ft/s as the acceleration due to gravity. Pay close attention to the units. u(t) = 5 cos (4 3 t) + sin(4V3 t) 2V3 b. Determine the period, amplitude...
3. < Previous Ne A mass weighing 9 lb stretches a spring 4 in. The mass is pulled down an additional 3 in and is then set in motion with an initial upward velocity of 6 ft/s. No damping is applied. a. Determine the position u of the mass at any time t. Use 32 ft/s as the acceleration due to gravity. Pay close attention to the units. u(t) = ft b. Determine the period, amplitude and phase of the...
A mass weighing 11 lb stretches a spring 8 in. The mass is attached to a viscous damper with damping constant 3 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 6 in/s. Determine the position u of the mass at any time t. Use 32 ft/s as the acceleration due to gravity. Pay close attention to the units. u(t) =
< Pre A mass weighing 18 lb stretches a spring 6 in. 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 4 in, and then set into motion with a downward velocity of 5 in/s. Determine the position u of the mass at any time t. Use 32 ft/s” as the acceleration due to gravity. Pay close attention to the units. u(t) = in
A mass weighing 10 lb stretches a spring 11 in. The mass is attached to a viscous damper with damping constant 3 lb ·s/ft. The mass is pushed upward, contracting the spring a distance of 4 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 as the acceleration due to gravity. Pay close attention to the units. u(t) =
A mass weighing 4 pounds stretches a spring 6 inches. At time t = 0, the weight is then struck to set it into motion with an initial velocity of 2 ft/sec, directed downward. Determine the equations of motion for the position and the velocity of the weight. Find the amplitude, period, and frequency of the position (displacement). A 4-lb weight stretches a spring 1 ft. If the weight moves in a medium where the magnitude of the damping force...
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...
A mass of 2 kg stretches a spring 40 cm. The mass is pulled downward 1m and released with an upwards velocity of 2m/s. Assuming there is no damping and that^1 the acceleration due to gravity is g = 10m/s^2, determine the position u(t) of the mass at time t, as well as the amplitude, period, frequency, and phase. Provide a rough sketch of the graph of the solution.
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