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A 2 kg mass stretches a spring 1 meter. The mass is pushed upward, con- tracting...
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?...
[2-25 pts) An 41b weight stretches a spring by 24 in. If the weight is pushed...
[2-25 pts) An 41b weight stretches a spring by 24 in. If the weight is pushed up and released 2 ft above the equilibrium with an upward velocity of 8 ft/s. Set up the IVP for this spring mass system. Solve this IVP and rewrite your solution into a single sinusoid. Then, find the amplitude, period, and initial phase of the motion. Find the 3rd time when the weight reaches the highest point. How many times the weight will reach...
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 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
5. A 2 kg mass is attached to a spring whose constant is 30 N/m, and the entire system is submerg...
5. A 2 kg mass is attached to a spring whose constant is 30 N/m, and the entire system is submerged in a liquid that imparts a damping force equal to 12 times the instaataneous velocity (a) Write the second-order linear differential equation to umodel the motion (b) Convert the second-order linear differential equation from part (a) to a first-order linear system (c) Classify the critical (equilibrium) point (0.0) (d) Sketch the phase portrait (e) Indicate the initial condition x(0)-(...
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...
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...
8. A10 kg mass stretches a spring 70 cm in equilibrium. Suppose a 2 kg mass...
8. A10 kg mass stretches a spring 70 cm in equilibrium. Suppose a 2 kg mass is attached to the spring, initially displaced 25 cmbelow equilibrium, and given an upward velocity of 2 m/s Find its displacement for t > 0. Find the frequency, period, amplitude, and phase angle of the motion.
[2-25 pts) An 41b weight stretches a spring by 24 in. If the weight is pushed up and released 2 ft above the equilibrium with an upward velocity of 8 ft/s. Set up the IVP for this spring mass system. Solve this IVP and rewrite your solution into a single sinusoid. Then, find the amplitude, period, and initial phase of the motion. Find the 3rd time when the weight reaches the highest point. How many times the weight will reach...
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 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
5. A 2 kg mass is attached to a spring whose constant is 30 N/m, and the entire system is submerged in a liquid that imparts a damping force equal to 12 times the instaataneous velocity (a) Write the second-order linear differential equation to umodel the motion (b) Convert the second-order linear differential equation from part (a) to a first-order linear system (c) Classify the critical (equilibrium) point (0.0) (d) Sketch the phase portrait (e) Indicate the initial condition x(0)-(...
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...
8. A10 kg mass stretches a spring 70 cm in equilibrium. Suppose a 2 kg mass is attached to the spring, initially displaced 25 cmbelow equilibrium, and given an upward velocity of 2 m/s Find its displacement for t > 0. Find the frequency, period, amplitude, and phase angle of the motion.
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