A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 spring system is disturbed from its rest state by the force F(t) = 40 cos(8t). The force F(t) is expressed in Newtons and is positive in the ward direction, and time is measured in seconds. Determine the spring constant k. k= Newtons / meter 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) = and y'(0) = help (equations) help (numbers)
A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 spring system is disturbed from its rest state by the force F(t) = 40 cos(8t). The force F(t) is expressed in Newtons and is positive in the ward direction, and time is measured in seconds. Determine the spring constant k. k= Newtons / meter 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) = and y'(0) = help (equations) help (numbers)
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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) = 40 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)
d. Plot the solution and determine the maximum excursion from equilibrium made by the object on the time interval 0 < t <co. If there is no such
maximum, enter NONE.
maximum excursion =
meters help (numbers)
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