Is this project an undergraduate, graduate, or faculty project?
Undergraduate
Project Type
group
Campus
Daytona Beach
Authors' Class Standing
Ashlynn Deadrick, Junior Will Standish, Tanay Agarwal
Lead Presenter's Name
Ashlynn Deadrick
Lead Presenter's College
DB College of Engineering
Faculty Mentor Name
Dr. Jorge Gonzalez
Abstract
Mechanical vibrations occur in many engineering systems and can be described using second-order differential equations. In this project, the motion of vibrating systems is studied using the mass–spring model. The focus is on three types of oscillations: free vibrations, dampened vibrations, and forced oscillations. Free vibration describes how a system moves when it is displaced and then released without any external force. Damped vibration includes effects such as friction or resistance that cause the motion to gradually decrease over time. Forced oscillations occur when an external force acts on the system and continuously drives the motion. This project also examines the effects of resonance and beats. Resonance happens when the frequency of an external force is close to the natural frequency of the system, which can cause very large oscillations. Beats occur when two frequencies are close together and create a pattern where the amplitude increases and decreases periodically. By solving and analyzing second-order linear differential equations, this project demonstrates how differential equations can be used to model and understand vibration behavior in mechanical systems.
Did this research project receive funding support (Spark, SURF, Research Abroad, Student Internal Grants, Collaborative, Climbing, or Ignite Grants) from the Office of Undergraduate Research?
No
Included in
Applied Mechanics Commons, Dynamics and Dynamical Systems Commons, Ordinary Differential Equations and Applied Dynamics Commons
Mechanical Vibrations and Damping
Mechanical vibrations occur in many engineering systems and can be described using second-order differential equations. In this project, the motion of vibrating systems is studied using the mass–spring model. The focus is on three types of oscillations: free vibrations, dampened vibrations, and forced oscillations. Free vibration describes how a system moves when it is displaced and then released without any external force. Damped vibration includes effects such as friction or resistance that cause the motion to gradually decrease over time. Forced oscillations occur when an external force acts on the system and continuously drives the motion. This project also examines the effects of resonance and beats. Resonance happens when the frequency of an external force is close to the natural frequency of the system, which can cause very large oscillations. Beats occur when two frequencies are close together and create a pattern where the amplitude increases and decreases periodically. By solving and analyzing second-order linear differential equations, this project demonstrates how differential equations can be used to model and understand vibration behavior in mechanical systems.