A 10 kilogram object suspended from the end of a vertically hanging spring 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 stretches the spring 9.8 centimeters. At time t = Newtons and is positive in the downward direction, and time is measured in seconds. Determine the spring constant k. k = Newtons / meter help (numbers) Hint is to use earth gravity of 9.8 meters per second squared, and note that Newton is kg meter per second squared. Formulate the initial value problem for x(t), where x(t) is the displacement of the object from its equilibrium rest state, measured positive in the downward direction. Give your answer in terms of x, x' , x" , t. Differential equation: help (equations) Initial conditions: x(0) = and x' (0) = help (numbers) Solve the initial value problem for x(t). x(t) = help (formulas) %3D Plot the solution and determine the maximum displacement from equilibrium made by the object on the time interval 0
A 10 kilogram object suspended from the end of a vertically hanging spring 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 stretches the spring 9.8 centimeters. At time t = Newtons and is positive in the downward direction, and time is measured in seconds. Determine the spring constant k. k = Newtons / meter help (numbers) Hint is to use earth gravity of 9.8 meters per second squared, and note that Newton is kg meter per second squared. Formulate the initial value problem for x(t), where x(t) is the displacement of the object from its equilibrium rest state, measured positive in the downward direction. Give your answer in terms of x, x' , x" , t. Differential equation: help (equations) Initial conditions: x(0) = and x' (0) = help (numbers) Solve the initial value problem for x(t). x(t) = help (formulas) %3D Plot the solution and determine the maximum displacement from equilibrium made by the object on the time interval 0
Related questions
Question
100%
Transcribed Image Text:A 10 kilogram object suspended from the end of a vertically hanging spring
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
stretches the spring 9.8 centimeters. At time t =
Newtons and is positive in the downward direction, and time is measured in seconds.
Determine the spring constant k.
k =
Newtons / meter help (numbers)
Hint is to use earth gravity of 9.8 meters per second squared, and note that Newton is kg
meter
per second squared.
Formulate the initial value problem for x(t), where x(t) is the displacement of the object from
its equilibrium rest state, measured positive in the downward direction.
Give your answer in terms of x, x' , x", t.
Differential equation:
help (equations)
Initial conditions: x(0) =
and x' (0) =
help (numbers)
Solve the initial value problem for x(t).
x(t) =
help (formulas)
Plot the solution and determine the maximum displacement from equilibrium made by the
object on the time interval 0 <t<∞. If there is no such maximum, enter "NONE".
maximum displacement
meters help (numbers)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 1 images
