mh" +5h' +120h = mg h(0)=100 h'(o)=0
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
How to determine the equilibrium points of this linear nonhomogeneous second-order differential equation.
![The image contains a differential equation and initial conditions, which are often used in physics and engineering to model dynamic systems.
**Differential Equation:**
\[ mh'' + 5h' + 12h = mg \]
This is a second-order linear differential equation with constant coefficients. In this expression:
- \( m \) represents mass.
- \( h \) is a function of time, with \( h'' \) indicating the second derivative of \( h \) with respect to time (acceleration), \( h' \) indicating the first derivative of \( h \) with respect to time (velocity), and \( h \) the displacement.
- \( g \) represents gravitational acceleration.
**Initial Conditions:**
- \( h(0) = 100 \)
- \( h'(0) = 0 \)
These conditions specify the state of the system at time \( t = 0 \):
- \( h(0) = 100 \) indicates that the initial position is 100 units.
- \( h'(0) = 0 \) indicates that the initial velocity is zero.
Understanding and solving this equation involves applying techniques of solving differential equations, considering the initial conditions to determine the specific solution for the system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d0ee2cb-cfe2-4eb9-a097-d38324436758%2F485f4dd7-b01e-49fa-a2c4-5a5f1c2b5634%2Fpzp6zw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains a differential equation and initial conditions, which are often used in physics and engineering to model dynamic systems.
**Differential Equation:**
\[ mh'' + 5h' + 12h = mg \]
This is a second-order linear differential equation with constant coefficients. In this expression:
- \( m \) represents mass.
- \( h \) is a function of time, with \( h'' \) indicating the second derivative of \( h \) with respect to time (acceleration), \( h' \) indicating the first derivative of \( h \) with respect to time (velocity), and \( h \) the displacement.
- \( g \) represents gravitational acceleration.
**Initial Conditions:**
- \( h(0) = 100 \)
- \( h'(0) = 0 \)
These conditions specify the state of the system at time \( t = 0 \):
- \( h(0) = 100 \) indicates that the initial position is 100 units.
- \( h'(0) = 0 \) indicates that the initial velocity is zero.
Understanding and solving this equation involves applying techniques of solving differential equations, considering the initial conditions to determine the specific solution for the system.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
