Mass Damper System: Differential Equations in Mechanical Engineering
Doctor Gary Hall
Differential Equations
March 2013
Differential Equations in Mechanical Engineering
Often times college students question the courses they are required to take and the relevance they have to their intended career. As engineers and scientists we are taught, and even “wired” in a way, to question things through-out our lives. We question the way things work, such as the way the shocks in our car work to give us a smooth ride back and forth to school, or what really happens to an object as it falls through the air, even how that people can predict an approximate future population. These questions, and many more, can be answered and explained through different variations of differential equations. By explaining and answering even just one of these questions through different differential equations I will also be answering two other important questions. Why is differential equations required for many students and how does it apply in the career of a mechanical engineer?
First some background. What is a differential equation?
A differential equation is a mathematical statement that contains one or more derivatives. It states a relationship involving the rates of change of continuously changing quantities modeled by functions. They are used whenever a rate of change is known but the process
giving rise to it is not. The solution of a differential equation is generally a function whose derivatives satisfy the equation. (Merriam-Webster)
Differential equations can also be of varying orders and can depend on more than one variable if need be. These differential equations are important to engineering because they can help relate many crucial functions and help simulate real world problems and the effects outside variables have on them.
An example of this is a mass spring damper system. After interviewing Professor Keller I became aware of the differential equations involved in such a system. Keller said, “The reason why most engineering students
Differential Equations
March 2013
Differential Equations in Mechanical Engineering
Often times college students question the courses they are required to take and the relevance they have to their intended career. As engineers and scientists we are taught, and even “wired” in a way, to question things through-out our lives. We question the way things work, such as the way the shocks in our car work to give us a smooth ride back and forth to school, or what really happens to an object as it falls through the air, even how that people can predict an approximate future population. These questions, and many more, can be answered and explained through different variations of differential equations. By explaining and answering even just one of these questions through different differential equations I will also be answering two other important questions. Why is differential equations required for many students and how does it apply in the career of a mechanical engineer?
First some background. What is a differential equation?
A differential equation is a mathematical statement that contains one or more derivatives. It states a relationship involving the rates of change of continuously changing quantities modeled by functions. They are used whenever a rate of change is known but the process
giving rise to it is not. The solution of a differential equation is generally a function whose derivatives satisfy the equation. (Merriam-Webster)
Differential equations can also be of varying orders and can depend on more than one variable if need be. These differential equations are important to engineering because they can help relate many crucial functions and help simulate real world problems and the effects outside variables have on them.
An example of this is a mass spring damper system. After interviewing Professor Keller I became aware of the differential equations involved in such a system. Keller said, “The reason why most engineering students
Cited: "Dictionary: All Forms of a Word (noun, Verb, Etc.) Are Now Displayed on One Page." Merriam-Webster. Merriam-Webster, n.d. Web. 14 Mar. 2013. . Keller, Darl. "Differential Equations in Engineering." Telephone interview. 18 Feb. 2013. Yechout, Thomas R., and Steven L. Morris. "Aircraft Dynamic Stability." Introduction to Aircraft Flight Mechanics: Performance, Static Stability, Dynamic Stability, and Classical Feedback Control. Reston, VA: American Institute of Aeronautics and Astronautics, 2003. N. pag. Print