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(8t). The force F(t) is expressed in Newtons and is positive in the downward direction, and ime 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)
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(8t). The force F(t) is expressed in Newtons and is positive in the downward direction, and ime 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)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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) = 170 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 <t < o. If there is no such maximum, enter NONE.
maximum excursion =
meters help (numbers)
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