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We know that a force of 7.2 Newtons is required to stretch a certain spring 0.8...
Differential Equation problem We know that a force of 2.8 Newtons is required to stretch a certain spring 0.7 meters beyond its natural length. A 1.44-kg mass is attached to this spring and allowed t...
Differential Equation problem
We know that a force of 2.8 Newtons is required to stretch a certain spring 0.7 meters beyond its natural length. A 1.44-kg mass is attached to this spring and allowed to come to equilibrium. The mass-spring system is then set in motion by applying a push in the upward direction that gives the mass an initial velocity of 1.04 meters per second. Let y(t) represent the displacement of the mass above the equilibrium position t seconds...
(1 point) A frictionless spring with a 7-kg mass can be held stretched 0.6 meters beyond...
(1 point) A frictionless spring with a 7-kg mass can be held stretched 0.6 meters beyond its natural length by a force of 70 newtons. If the spring begins at its equilibrium position, but a push gives it an initial velocity of 1 m/sec, find the position of the mass after t seconds. 0.244sin(4.08t) meters
3) Consider Hooke's Law: The force required to keep a spring in a compressed or stretched position x units from the spring's equilibrium position is F(x)-kr Calculate the work required, in jo...
3) Consider Hooke's Law: The force required to keep a spring in a compressed or stretched position x units from the spring's equilibrium position is F(x)-kr Calculate the work required, in joules, to stretch a spring 0.4 meters beyond its equilibrium position for each of the following scenarios. a) The spring requires 50 Newtons of force to hold it 0.1 m from its equilibrium position. b) The spring requires 2 Joules of work to stretch the spring 0.1 meter from...
find the general solution (y) using laplace transform (1 point) Consider a spring attached to a...
find the general solution (y) using laplace transform
(1 point) Consider a spring attached to a 1 kg mass, damping constant 8 = 5, and spring constant k = 6 The initial position of the spring is 4 metres beyond its resting length, and the initial velocity is -9 m/s. After 1 second, a constant force of 12 Newtons is applied to the system for exactly 2 seconds Set up a differential equation for the position of the spring y...
2. A spring is stretched 10 cm by a force of 3 newtons. A mass of...
2. A spring is stretched 10 cm by a force of 3 newtons. A mass of 2 kg is hung from the spring and is also attached to a viscous damper that exerts a force of 3 newtons when the velocity of the mass is 5 m/sec. If the mass is pulled down 5 cm below its equilibrium position and given an initial downward velocity of 10 cm/sec, determine its position u at time t. Find the quasi frequency and...
A block with mass m =7.2 kg is hung from a vertical spring. When the mass...
A block with mass m =7.2 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.25 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.6 m/s. The block oscillates on the spring without friction. What is the spring constant of the spring? What is the oscillation frequency? After t = 0.39 s what is the speed of the block? What is...
(1 point) A spring-mass system with a 5-kg mass and a damping constant 8-N sec/m can...
(1 point) A spring-mass system with a 5-kg mass and a damping constant 8-N sec/m can be held stretched 0.5 meters beyond its natural length by a force of 2.5 newtons. Suppose the spring is stretched 1 meters beyond its natural length and then released with zero velocity, In the notation of the text, what is the value y2 – 4mk? Find the position of the mass after t seconds. Your answer should be a function of the variable t...
4. A spring is stretch 10 cm by a force of 3 N. A mass of...
4. A spring is stretch 10 cm by a force of 3 N. A mass of 2 kg is hung from the spring and is also attached to a viscous damper that exerts a force of 3 N when the velocity of the mass is 5 m/s. If the mass is pulled down 5 cm below its equilibrium position and given an initial donward velocity of 10 cm/s determine its position u at any time t. Find the quasi-frequency μ...
(1 point) Consider a spring attached to a 1 kg mass, damping constant 6 = 9,...
(1 point) Consider a spring attached to a 1 kg mass, damping constant 6 = 9, and spring constant k = 20. The initial position of the spring is -1 metres beyond its resting length, and the initial velocity is 2 m/s. After 1 second, a constant force of 60 Newtons is applied to the system for exactly 2 seconds. Set up a differential equation for the position of the spring y (in metres beyond its resting length) after t...
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...
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...
Differential Equation problem
We know that a force of 2.8 Newtons is required to stretch a certain spring 0.7 meters beyond its natural length. A 1.44-kg mass is attached to this spring and allowed to come to equilibrium. The mass-spring system is then set in motion by applying a push in the upward direction that gives the mass an initial velocity of 1.04 meters per second. Let y(t) represent the displacement of the mass above the equilibrium position t seconds...
(1 point) A frictionless spring with a 7-kg mass can be held stretched 0.6 meters beyond its natural length by a force of 70 newtons. If the spring begins at its equilibrium position, but a push gives it an initial velocity of 1 m/sec, find the position of the mass after t seconds. 0.244sin(4.08t) meters
3) Consider Hooke's Law: The force required to keep a spring in a compressed or stretched position x units from the spring's equilibrium position is F(x)-kr Calculate the work required, in joules, to stretch a spring 0.4 meters beyond its equilibrium position for each of the following scenarios. a) The spring requires 50 Newtons of force to hold it 0.1 m from its equilibrium position. b) The spring requires 2 Joules of work to stretch the spring 0.1 meter from...
find the general solution (y) using laplace transform
(1 point) Consider a spring attached to a 1 kg mass, damping constant 8 = 5, and spring constant k = 6 The initial position of the spring is 4 metres beyond its resting length, and the initial velocity is -9 m/s. After 1 second, a constant force of 12 Newtons is applied to the system for exactly 2 seconds Set up a differential equation for the position of the spring y...
2. A spring is stretched 10 cm by a force of 3 newtons. A mass of 2 kg is hung from the spring and is also attached to a viscous damper that exerts a force of 3 newtons when the velocity of the mass is 5 m/sec. If the mass is pulled down 5 cm below its equilibrium position and given an initial downward velocity of 10 cm/sec, determine its position u at time t. Find the quasi frequency and...
A block with mass m =7.2 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.25 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.6 m/s. The block oscillates on the spring without friction. What is the spring constant of the spring? What is the oscillation frequency? After t = 0.39 s what is the speed of the block? What is...
(1 point) A spring-mass system with a 5-kg mass and a damping constant 8-N sec/m can be held stretched 0.5 meters beyond its natural length by a force of 2.5 newtons. Suppose the spring is stretched 1 meters beyond its natural length and then released with zero velocity, In the notation of the text, what is the value y2 – 4mk? Find the position of the mass after t seconds. Your answer should be a function of the variable t...
4. A spring is stretch 10 cm by a force of 3 N. A mass of 2 kg is hung from the spring and is also attached to a viscous damper that exerts a force of 3 N when the velocity of the mass is 5 m/s. If the mass is pulled down 5 cm below its equilibrium position and given an initial donward velocity of 10 cm/s determine its position u at any time t. Find the quasi-frequency μ...
(1 point) Consider a spring attached to a 1 kg mass, damping constant 6 = 9, and spring constant k = 20. The initial position of the spring is -1 metres beyond its resting length, and the initial velocity is 2 m/s. After 1 second, a constant force of 60 Newtons is applied to the system for exactly 2 seconds. Set up a differential equation for the position of the spring y (in metres beyond its resting length) after t...
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...
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