1. Mechanical Vibrations 2DoF Vibration Systems
Philadelphia University
Engineering Faculty
Mechanical Engineering Department
Professor Adnan Dawood Mohammed

2. Two degrees of freedom system
Examples
2 DoF : x(t) and θ(t)

3. Two degrees of freedom system
Examples
DoF : x(t) and y(t)

4. General physical system: Consider the masses springs system shown:
Equations of motion
General physical system:
Consider the masses springs system shown:
Figure (1)
The equations of motion can be obtained using Newton’s second law as follows:

17. Lagrange’s Equation