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) = 80 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 = 1000 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: y"+100y = 8cos(8t) help (equations) Initial conditions: y(0) = 0 and y'(0) = 0 help (numbers) c. Solve the initial value problem for y(t). y(t) = (5/18)(cos8t-cos10t) 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) = 80 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 = 1000 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: y"+100y = 8cos(8t) help (equations) Initial conditions: y(0) = 0 and y'(0) = 0 help (numbers) c. Solve the initial value problem for y(t). y(t) = (5/18)(cos8t-cos10t) help (formulas) d. Plot the solution and determine the maximum excursion from equilibrium made by the object on the time interval 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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) = 80 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 = 1000
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: y"+100y = 8cos(8t)
help (equations)
Initial conditions: y(0) = 0
and y'(0) = 0
help (numbers)
c. Solve the initial value problem for y(t).
y(t) = (5/18)(cos8t-cos10t)
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
no
such maximum, enter NONE.
maximum excursion =
0.58
meters help (numbers)
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