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An object of mass 4 grams hanging at the bottom of a spring with a spring...
Part C An object of mass 4 grams hanging at the bottom of a spring with...
Part C
An object of mass 4 grams hanging at the bottom of a spring with a spring constant 3 grams per second square. Denote by y vertical coordinate, positive downwards, and y 0 is the spring-mass resting position. g(t) (a) Write the differential equation satisfied by this system. Note: Write t for t, write y for y(), and yp for y () (b) Find the mechanical energy E of this system. Note: Write t for t, write y for...
second square is moving in a liquid with damping constant 3 grams per second. Denote by...
second square is moving in a liquid with damping constant 3 grams per second. Denote by y vertical coordinate, positive downwards, and y 0 is the spring-mass resting position. (a) Write the differential equation satisfied by this system. y" Note: Write t for t, write y for y(t), and yp for y' (t). (b) Find the mechanical energy E of this system E(t) Note: Write t for t, write y for y(t), and yp for y' (t). (c) Find the...
An object of mass 3 grams is attached to a vertical spring with spring constant 27...
An object of mass 3 grams is attached to a vertical spring with spring constant 27 grams/seca. Neglect any friction with the air. (a) Find the differential equation y = fly, y) satisfied by the function y, the displacement of the object from its equilibrium position, positive downwards. Write y for y(t) and yp for y' (t). y = (b) Find rı,r2, roots of the characteristic polynomial of the equation above. ru,r2 = (b) Find a set of real-valued fundamental...
An object of mass 33 grams is attached to a vertical spring with spring constant 48grams/sec248grams/sec2....
An object of mass 33 grams is attached to a vertical spring with
spring constant 48grams/sec248grams/sec2. Neglect any friction with
the air.
Problem Value: 10 point(s). Problem Score: 0%. Attempts Remaining: 25 attempts. Help Entering Answers See Example 2.2.7, in Section 2.2, in the MTH 235 Lecture Notes. (10 points) An object of mass 3 grams is attached to a vertical spring with spring constant 48 grams/sec. Neglect any friction with the air. (a) Find the differential equation y' =...
An object of mass m 5 kilograms falls vertically to the ground under the action of...
An object of mass m 5 kilograms falls vertically to the ground under the action of the earth gravitational acceleration of magnitude g 10 meters per second squared. Denote by y vertical coordinate, positive upwards, and let y 0 be at the earth surface. Recall that the force on the object in this situation is f--mg, where the negative sign says the force points downwards. (a) Write the differential equation satisfied by this system. y"-10 Note: Write t for t,...
A 189-kg mass, when attached to the end of a spring hanging vertically, stretches the spring...
A 189-kg mass, when attached to the end of a spring hanging vertically, stretches the spring 9 m. The mass is in a medium that exerts a viscous resistance of 3024 N when the mass has a velocity of 4 m/sec. Assume the mass is given an initial velocity of 14 m/s from the equilibrium position. a) Determine the spring constant k. Use g = 10 m/sec. k b) Determine the damping coeffient 7. 7 c) If the initial value...
A 288-kg mass, when attached to the end of a spring hanging vertically, stretches the spring...
A 288-kg mass, when attached to the end of a spring hanging vertically, stretches the spring 8 m. The mass is in a medium that exerts a viscous resistance of 576 N when the mass has a velocity of 4 m/sec. Assume the mass is given an initial velocity of 18 m/s from the equilibrium position. a) Determine the spring constant k. Use g = 10 m/sec. k b) Determine the damping coeffient 7. 7= c) If the initial value...
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...
(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...
(1 point) A 10 kilogram object suspended from the end of a vertically hanging spring stretches th...
(1 point) A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time 0, the resulting mass- spring system is disturbed from its rest state by the force F(t) 70 cos(8t). 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 Newtons/meter b. Formulate the initial value problem for y(), where y(t) is the displacement...
Part C
An object of mass 4 grams hanging at the bottom of a spring with a spring constant 3 grams per second square. Denote by y vertical coordinate, positive downwards, and y 0 is the spring-mass resting position. g(t) (a) Write the differential equation satisfied by this system. Note: Write t for t, write y for y(), and yp for y () (b) Find the mechanical energy E of this system. Note: Write t for t, write y for...
second square is moving in a liquid with damping constant 3 grams per second. Denote by y vertical coordinate, positive downwards, and y 0 is the spring-mass resting position. (a) Write the differential equation satisfied by this system. y" Note: Write t for t, write y for y(t), and yp for y' (t). (b) Find the mechanical energy E of this system E(t) Note: Write t for t, write y for y(t), and yp for y' (t). (c) Find the...
An object of mass 3 grams is attached to a vertical spring with spring constant 27 grams/seca. Neglect any friction with the air. (a) Find the differential equation y = fly, y) satisfied by the function y, the displacement of the object from its equilibrium position, positive downwards. Write y for y(t) and yp for y' (t). y = (b) Find rı,r2, roots of the characteristic polynomial of the equation above. ru,r2 = (b) Find a set of real-valued fundamental...
An object of mass 33 grams is attached to a vertical spring with
spring constant 48grams/sec248grams/sec2. Neglect any friction with
the air.
Problem Value: 10 point(s). Problem Score: 0%. Attempts Remaining: 25 attempts. Help Entering Answers See Example 2.2.7, in Section 2.2, in the MTH 235 Lecture Notes. (10 points) An object of mass 3 grams is attached to a vertical spring with spring constant 48 grams/sec. Neglect any friction with the air. (a) Find the differential equation y' =...
An object of mass m 5 kilograms falls vertically to the ground under the action of the earth gravitational acceleration of magnitude g 10 meters per second squared. Denote by y vertical coordinate, positive upwards, and let y 0 be at the earth surface. Recall that the force on the object in this situation is f--mg, where the negative sign says the force points downwards. (a) Write the differential equation satisfied by this system. y"-10 Note: Write t for t,...
A 189-kg mass, when attached to the end of a spring hanging vertically, stretches the spring 9 m. The mass is in a medium that exerts a viscous resistance of 3024 N when the mass has a velocity of 4 m/sec. Assume the mass is given an initial velocity of 14 m/s from the equilibrium position. a) Determine the spring constant k. Use g = 10 m/sec. k b) Determine the damping coeffient 7. 7 c) If the initial value...
A 288-kg mass, when attached to the end of a spring hanging vertically, stretches the spring 8 m. The mass is in a medium that exerts a viscous resistance of 576 N when the mass has a velocity of 4 m/sec. Assume the mass is given an initial velocity of 18 m/s from the equilibrium position. a) Determine the spring constant k. Use g = 10 m/sec. k b) Determine the damping coeffient 7. 7= c) If the initial value...
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...
(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...
(1 point) A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time 0, the resulting mass- spring system is disturbed from its rest state by the force F(t) 70 cos(8t). 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 Newtons/meter b. Formulate the initial value problem for y(), where y(t) is the displacement...
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