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(1 point) A 10 kilogram object suspended from the end of a vertically hanging spring stretches th...
(10 pts) A 10 kilogram object suspended from the end of a vertically hanging spring stretches...
(10 pts) A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time t = 0, the resulting mass-spring system is disturbed from its rest state by the force F(t) = 170 cos(10t). The force F(t) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds. a. Determine the spring constant k. k = 1000 Newtons / meter b. Formulate the initial value problem...
A 10 10 kilogram object suspended from the end of a vertically hanging spring stretches the...
A 10 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 9.8 centimeters. At time ?=0 t = 0 , the resulting mass-spring system is disturbed from its rest state by the force ?(?)=150cos(10?) F ( t ) = 150 cos ( 10 t ) . The force ?(?) F ( t ) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds. Solve the initial...
A 5 kilogram mass suspended from the end of a vertical spring stretches it by 1.225 metres. The system is placed in a medium offering a resistance (in Newtons) equal to 45 times the instantaneous vel...
A 5 kilogram mass suspended from the end of a vertical spring stretches it by 1.225 metres. The system is placed in a medium offering a resistance (in Newtons) equal to 45 times the instantaneous velocity (in m/s). The mass is started in motion from the equilibrium position with an initial velocity of 1 m/s in the upward direction and with an applied external force F(t) 365 cos(3t) Newtons downwards. The displacement of the mass below the equilibrium position at...
(1 point) A steel ball weighing 128 pounds is suspended from a spring. This stretches the...
(1 point) A steel ball weighing 128 pounds is suspended from a spring. This stretches the spring feet. The ball is started in motion from the equilibrium position with a downward velocity of 3 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second). Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that this means...
(1 point) A steel ball weighing 128 pounds is suspended from a spring This stretches the...
(1 point) A steel ball weighing 128 pounds is suspended from a spring This stretches the spring 13 feet The ball is started in motion from the equilibrium position with a downward velocity of 9 feet per second The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) Suppose that after t seconds the ball is y feet below its rest position Find y in terms of t. (Note that this...
DIFFERENTIAL EQUATIONS An object stretches a spring 6 inches when it comes to rest at equilibrium....
DIFFERENTIAL EQUATIONS
An object stretches a spring 6 inches when it comes to rest at
equilibrium. Find its displacement for t > 0 if it is initially
displaced 3 inches above equilibrium and given a downward velocity
of 6 inches per second.
Use substitution :
Answer:y= -1/4 cos(8t)+1/16 sin(8t)
(1 point) A steel ball weighing 128 pounds is suspended from a spring. This stretches the...
(1 point) A steel ball weighing 128 pounds is suspended from a spring. This stretches the spring 128 257 feet. The ball is started in motion from the equilibrium position with a downward velocity of 3 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second). Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that...
145 (1 point) A steel ball weighing 128 pounds is suspended from a spring. This stretches...
145 (1 point) A steel ball weighing 128 pounds is suspended from a spring. This stretches the spring 128 feet The ball is started in motion from the equilibrium position with a downward velocity of 7 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second). Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that...
A 1 kg object is attached to a spring and stretches it 0.2 m on its...
A 1 kg object is attached to a spring and stretches it 0.2 m on its own. There is no damping in the system, but an external force is present, described by the function F(t) = 6 cos omega t. The object is initially displaced 30 cm downward from equilibrium with no initial velocity and system experiences resonance. Find the displacement of the object at any time t.
An object of weight 6 Newton stretches a vertically hanging spring by 3/20 meter. Then this...
An object of weight 6 Newton stretches a vertically hanging spring by 3/20 meter. Then this object is replaced by another object of mass 4 kilogram and whole mass- spring system is submerged in a liquid that provides 72 Newton of frictional force for each 3 meter/second velocity. Now this object is pulled down 12 meter below its static equilibrium position and set in motion with an upward velocity of 31 meter/second. Which of the following options is the time...
(10 pts) A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time t = 0, the resulting mass-spring system is disturbed from its rest state by the force F(t) = 170 cos(10t). The force F(t) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds. a. Determine the spring constant k. k = 1000 Newtons / meter b. Formulate the initial value problem...
A 5 kilogram mass suspended from the end of a vertical spring stretches it by 1.225 metres. The system is placed in a medium offering a resistance (in Newtons) equal to 45 times the instantaneous velocity (in m/s). The mass is started in motion from the equilibrium position with an initial velocity of 1 m/s in the upward direction and with an applied external force F(t) 365 cos(3t) Newtons downwards. The displacement of the mass below the equilibrium position at...
(1 point) A steel ball weighing 128 pounds is suspended from a spring. This stretches the spring feet. The ball is started in motion from the equilibrium position with a downward velocity of 3 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second). Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that this means...
(1 point) A steel ball weighing 128 pounds is suspended from a spring This stretches the spring 13 feet The ball is started in motion from the equilibrium position with a downward velocity of 9 feet per second The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) Suppose that after t seconds the ball is y feet below its rest position Find y in terms of t. (Note that this...
DIFFERENTIAL EQUATIONS
An object stretches a spring 6 inches when it comes to rest at
equilibrium. Find its displacement for t > 0 if it is initially
displaced 3 inches above equilibrium and given a downward velocity
of 6 inches per second.
Use substitution :
Answer:y= -1/4 cos(8t)+1/16 sin(8t)
(1 point) A steel ball weighing 128 pounds is suspended from a spring. This stretches the spring 128 257 feet. The ball is started in motion from the equilibrium position with a downward velocity of 3 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second). Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that...
145 (1 point) A steel ball weighing 128 pounds is suspended from a spring. This stretches the spring 128 feet The ball is started in motion from the equilibrium position with a downward velocity of 7 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second). Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that...
A 1 kg object is attached to a spring and stretches it 0.2 m on its own. There is no damping in the system, but an external force is present, described by the function F(t) = 6 cos omega t. The object is initially displaced 30 cm downward from equilibrium with no initial velocity and system experiences resonance. Find the displacement of the object at any time t.
An object of weight 6 Newton stretches a vertically hanging spring by 3/20 meter. Then this object is replaced by another object of mass 4 kilogram and whole mass- spring system is submerged in a liquid that provides 72 Newton of frictional force for each 3 meter/second velocity. Now this object is pulled down 12 meter below its static equilibrium position and set in motion with an upward velocity of 31 meter/second. Which of the following options is the time...
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