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A 9 kilogram object suspended from the end of a vertically hanging spring stretches the spring 61.25 centimeters. At time t = 0, the resulting mass- spring system is disturbed from its rest state by the force F(t) = 18 cos(4t). The force F(t) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds. Determine the spring constant k. k = Newtons / meter help (numbers) Hint is to use earth gravity of 9.8 meters per second squared, and note that Newton is kg meter per second squared. Formulate the initial value problem for x(t), where x(t) is the displacement of the object from its equilibrium rest state, measured positive in the downward direction. Give your answer in terms of x, x', x", t. Differential equation: help (equations) Initial conditions: x(0) and æ'(0) help (numbers) Solve the initial value problem for æ(t). x(t) help (formulas) Plot the solution and determine the maximum displacement from equilibrium made by the object on the time interval 0

A 9 kilogram object suspended from the end of a vertically hanging spring stretches the spring 61.25 centimeters. At time t = 0, the resulting mass- spring system is disturbed from its rest state by the force F(t) = 18 cos(4t). The force F(t) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds. Determine the spring constant k. k = Newtons / meter help (numbers) Hint is to use earth gravity of 9.8 meters per second squared, and note that Newton is kg meter per second squared. Formulate the initial value problem for x(t), where x(t) is the displacement of the object from its equilibrium rest state, measured positive in the downward direction. Give your answer in terms of x, x', x", t. Differential equation: help (equations) Initial conditions: x(0) and æ'(0) help (numbers) Solve the initial value problem for æ(t). x(t) help (formulas) Plot the solution and determine the maximum displacement from equilibrium made by the object on the time interval 0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.3: Quadratic Equations
Problem 52E
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A9 kilogram object suspended from the end of a vertically hanging spring stretches the spring 61.25 centimeters. At time t = 0, the resulting mass- spring system is disturbed from its rest state by the force F(t) = 18 cos(4t). The force F(t) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds. Determine the spring constant k. k = Newtons / meter help (numbers) Hint is to use earth gravity of 9.8 meters per second squared, and note that Newton is kg meter per second squared. Formulate the initial value problem for æ(t), where x(t) is the displacement of the object from its equilibrium rest state, measured positive in the downward direction. Give your answer in terms of x, x', x", t. Differential equation: help (equations) Initial conditions: x(0) and æ'(0) help (numbers) Solve the initial value problem for æ(t). x(t) help (formulas) Plot the solution and determine the maximum displacement from equilibrium made by the object on the time interval 0 <t<o. If there is no such maximum, enter "NONE". maximum displacement = meters help (numbers)
Transcribed Image Text:A9 kilogram object suspended from the end of a vertically hanging spring stretches the spring 61.25 centimeters. At time t = 0, the resulting mass- spring system is disturbed from its rest state by the force F(t) = 18 cos(4t). The force F(t) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds. Determine the spring constant k. k = Newtons / meter help (numbers) Hint is to use earth gravity of 9.8 meters per second squared, and note that Newton is kg meter per second squared. Formulate the initial value problem for æ(t), where x(t) is the displacement of the object from its equilibrium rest state, measured positive in the downward direction. Give your answer in terms of x, x', x", t. Differential equation: help (equations) Initial conditions: x(0) and æ'(0) help (numbers) Solve the initial value problem for æ(t). x(t) help (formulas) Plot the solution and determine the maximum displacement from equilibrium made by the object on the time interval 0 <t<o. If there is no such maximum, enter "NONE". maximum displacement = meters help (numbers)
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