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 disturbed from its rest state by the force F(t)= 150 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: Initial conditions: y(0) c. Solve the initial value problem for y(t). y(t) = and y'(0) = help (equations) help (numbers) help (formulas)
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 disturbed from its rest state by the force F(t)= 150 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: Initial conditions: y(0) c. Solve the initial value problem for y(t). y(t) = and y'(0) = help (equations) help (numbers) help (formulas)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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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) 150 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 =
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:
Initial conditions: y(0) =
Newtons / meter
c. Solve the initial value problem for y(t).
y(t)
=
and y'(0)
=
help (equations)
help (numbers)
help (formulas)
d. Plot the solution and determine the maximum excursion from equilibrium made by the object on the time interval 0 < t < ∞. If there is no such maximum,
enter NONE.
maximum excursion =
meters help (numbers)
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