The image contains a differential equation and a graph representation. The handwritten equation is: \[ my'' + 5y' + 120y = mg \] Where: - \( m \) is a constant. - \( y'' \) is the second derivative of \( y \) with respect to time, denoting acceleration. - \( y' \) is the first derivative of \( y \), denoting velocity. - \( y \) is the position function. - \( g \) represents acceleration due to gravity. On the right, there is a horizontal line with labels: - The line is marked at \( 100 \) and \( y(0) = \), suggesting an initial value problem or a specific condition at \( t = 0 \). - Below the line, numbers are marked at intervals of \( 0 \), \( 25 \), and \( 75 \), likely indicating some form of scale or measurement points. This setup could be used in a lecture or lesson on solving differential equations, particularly second-order linear ordinary differential equations with constant coefficients.
The image contains a differential equation and a graph representation. The handwritten equation is: \[ my'' + 5y' + 120y = mg \] Where: - \( m \) is a constant. - \( y'' \) is the second derivative of \( y \) with respect to time, denoting acceleration. - \( y' \) is the first derivative of \( y \), denoting velocity. - \( y \) is the position function. - \( g \) represents acceleration due to gravity. On the right, there is a horizontal line with labels: - The line is marked at \( 100 \) and \( y(0) = \), suggesting an initial value problem or a specific condition at \( t = 0 \). - Below the line, numbers are marked at intervals of \( 0 \), \( 25 \), and \( 75 \), likely indicating some form of scale or measurement points. This setup could be used in a lecture or lesson on solving differential equations, particularly second-order linear ordinary differential equations with constant coefficients.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
A linear second-order non-homogeneous equation models this scenario: People falling at a height of 100ft above the ground attached to a 100-foot rope into a pit that's 25 ft deep and 75 feet from ground level. Spring constant of the rope is 120 lbs/ft, and air resistance is 5 times the instantaneous velocity. M is mass of person and g is gravity. Note that the pit is actually 100 ft in height: 75 from ground level plus 25 ft deep. Write this scenario as an initial value problem in matrix form. The equation is my''+5y'+120y=mg
![The image contains a differential equation and a graph representation. The handwritten equation is:
\[ my'' + 5y' + 120y = mg \]
Where:
- \( m \) is a constant.
- \( y'' \) is the second derivative of \( y \) with respect to time, denoting acceleration.
- \( y' \) is the first derivative of \( y \), denoting velocity.
- \( y \) is the position function.
- \( g \) represents acceleration due to gravity.
On the right, there is a horizontal line with labels:
- The line is marked at \( 100 \) and \( y(0) = \), suggesting an initial value problem or a specific condition at \( t = 0 \).
- Below the line, numbers are marked at intervals of \( 0 \), \( 25 \), and \( 75 \), likely indicating some form of scale or measurement points.
This setup could be used in a lecture or lesson on solving differential equations, particularly second-order linear ordinary differential equations with constant coefficients.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d0ee2cb-cfe2-4eb9-a097-d38324436758%2Fc0488eb8-c026-4e5b-ab1b-bd651eba21c6%2Fyotcxo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains a differential equation and a graph representation. The handwritten equation is:
\[ my'' + 5y' + 120y = mg \]
Where:
- \( m \) is a constant.
- \( y'' \) is the second derivative of \( y \) with respect to time, denoting acceleration.
- \( y' \) is the first derivative of \( y \), denoting velocity.
- \( y \) is the position function.
- \( g \) represents acceleration due to gravity.
On the right, there is a horizontal line with labels:
- The line is marked at \( 100 \) and \( y(0) = \), suggesting an initial value problem or a specific condition at \( t = 0 \).
- Below the line, numbers are marked at intervals of \( 0 \), \( 25 \), and \( 75 \), likely indicating some form of scale or measurement points.
This setup could be used in a lecture or lesson on solving differential equations, particularly second-order linear ordinary differential equations with constant coefficients.
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