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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) = 180 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. k= Newtons/meter b. Formulate the initial value problem for y(t), where y(t) is the displacement of the object from its equilibrium rest state, measured positive in the downward direction. (Give your answer in terms of y, y', y", t.) Differential equation: help (equations) Initial conditions: y(0) = == and y'(0) = help (numbers) c. Solve the initial value problem for y(t). y(t) = help (formulas) d. Plot the solution and determine the maximum excursion from equilibrium made by the object on the time interval 0

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) = 180 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. k= Newtons/meter b. Formulate the initial value problem for y(t), where y(t) is the displacement of the object from its equilibrium rest state, measured positive in the downward direction. (Give your answer in terms of y, y', y", t.) Differential equation: help (equations) Initial conditions: y(0) = == and y'(0) = help (numbers) c. Solve the initial value problem for y(t). y(t) = help (formulas) d. Plot the solution and determine the maximum excursion 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
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 73E
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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) = 180 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. k= Newtons/meter b. Formulate the initial value problem for y(t), where y(t) is the displacement of the object from its equilibrium rest state, measured positive in the downward direction. (Give your answer in terms of y, y', y", t.) Differential equation: help (equations) Initial conditions: y(0) = and y'(0) = help (numbers) c. Solve the initial value problem for y(t). (t)=help (formulas) d. Plot the solution and determine the maximum excursion from equilibrium made by the object on the time interval 0 too. If there is no such maximum, enter NONE. maximum excursion = meters help (numbers)
Transcribed Image Text: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) = 180 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. k= Newtons/meter b. Formulate the initial value problem for y(t), where y(t) is the displacement of the object from its equilibrium rest state, measured positive in the downward direction. (Give your answer in terms of y, y', y", t.) Differential equation: help (equations) Initial conditions: y(0) = and y'(0) = help (numbers) c. Solve the initial value problem for y(t). (t)=help (formulas) d. Plot the solution and determine the maximum excursion from equilibrium made by the object on the time interval 0 too. If there is no such maximum, enter NONE. maximum excursion = meters help (numbers)
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