1. FORCED UNDAMPED HARMONIC MOTION, w = wo Let us examine the case where the forcing frequency and the natural frequency of the oscil- lator are the same, x" + x = A cos(wot) For the case of a suspension bridge, we can think of the supporting cables as springs and that the wind or marching soldiers can create the external force on the bridge. If we take bridge roadway to have a mass of 1,000 kg, and the spring constant of the cables as 25,000 Newtons/meter, and further more supppose the wind or the soliders create an external force on the bridge of f(t) = 4000 cos(wt) Newtons, the equation (4) becomes which simplifies to 1000x" +25000x = 4000 cos(wt) x" + 25x= 4 cos(wt) (a) If the Method of Undetermined Coefficients is used to find the solution to the following intial value problem, What is the form of the trial solution? Here w= wo x" 25x4 cos(5t), x(0) = 0, x'(0) = 0. (b) Using computer software app, graph the solution to the IVP on [0, 20] and include the graph with your worksheet. (c) What does this this solution indicate about the behavior of the Millennium Bridge when the forcing term has a frequency that is the same as the natural frequency of the bridge.
1. FORCED UNDAMPED HARMONIC MOTION, w = wo Let us examine the case where the forcing frequency and the natural frequency of the oscil- lator are the same, x" + x = A cos(wot) For the case of a suspension bridge, we can think of the supporting cables as springs and that the wind or marching soldiers can create the external force on the bridge. If we take bridge roadway to have a mass of 1,000 kg, and the spring constant of the cables as 25,000 Newtons/meter, and further more supppose the wind or the soliders create an external force on the bridge of f(t) = 4000 cos(wt) Newtons, the equation (4) becomes which simplifies to 1000x" +25000x = 4000 cos(wt) x" + 25x= 4 cos(wt) (a) If the Method of Undetermined Coefficients is used to find the solution to the following intial value problem, What is the form of the trial solution? Here w= wo x" 25x4 cos(5t), x(0) = 0, x'(0) = 0. (b) Using computer software app, graph the solution to the IVP on [0, 20] and include the graph with your worksheet. (c) What does this this solution indicate about the behavior of the Millennium Bridge when the forcing term has a frequency that is the same as the natural frequency of the bridge.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![1. FORCED UNDAMPED HARMONIC MOTION, w = wo
Let us examine the case where the forcing frequency and the natural frequency of the oscil-
lator are the same,
x" + x =
A cos(wot)
For the case of a suspension bridge, we can think of the supporting cables as springs and
that the wind or marching soldiers can create the external force on the bridge. If we take
bridge roadway to have a mass of 1,000 kg, and the spring constant of the cables as 25,000
Newtons/meter, and further more supppose the wind or the soliders create an external force
on the bridge of f(t) = 4000 cos(wt) Newtons, the equation (4) becomes
which simplifies to
1000x" +25000x = 4000 cos(wt)
x" + 25x= 4 cos(wt)
(a) If the Method of Undetermined Coefficients is used to find the solution to the following
intial value problem, What is the form of the trial solution? Here w= wo
x" 25x4 cos(5t), x(0) = 0, x'(0) = 0.
(b) Using computer software app, graph the solution to the IVP on [0, 20] and include the
graph with your worksheet.
(c) What does this this solution indicate about the behavior of the Millennium Bridge
when the forcing term has a frequency that is the same as the natural frequency of the
bridge.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe55cfba9-7bce-45cb-a868-b9c474dd1b77%2F6b807162-2e13-495d-b34e-4120f8f1db9f%2Fzc1ssji_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. FORCED UNDAMPED HARMONIC MOTION, w = wo
Let us examine the case where the forcing frequency and the natural frequency of the oscil-
lator are the same,
x" + x =
A cos(wot)
For the case of a suspension bridge, we can think of the supporting cables as springs and
that the wind or marching soldiers can create the external force on the bridge. If we take
bridge roadway to have a mass of 1,000 kg, and the spring constant of the cables as 25,000
Newtons/meter, and further more supppose the wind or the soliders create an external force
on the bridge of f(t) = 4000 cos(wt) Newtons, the equation (4) becomes
which simplifies to
1000x" +25000x = 4000 cos(wt)
x" + 25x= 4 cos(wt)
(a) If the Method of Undetermined Coefficients is used to find the solution to the following
intial value problem, What is the form of the trial solution? Here w= wo
x" 25x4 cos(5t), x(0) = 0, x'(0) = 0.
(b) Using computer software app, graph the solution to the IVP on [0, 20] and include the
graph with your worksheet.
(c) What does this this solution indicate about the behavior of the Millennium Bridge
when the forcing term has a frequency that is the same as the natural frequency of the
bridge.
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