1. WEEK-2: Governing equation of SDOF systems
Assoc. Prof. Dr. Abdullah Seçgin

2. Governing equation (Equation of motion) of SDOF systems
a) By equivalent energy method

3. Example: Find equivalent stiffness using “Equivalent energy method”

4. Example: Find equivalent mass using “Equivalent energy method”

5. Example: Find equation of motion of the following system by using Equivalent energy method.

6. b) By Newton’s Second Law
Equation of motion
(Governing equation)

7. Free-Body Diagram (FBD)
System

8. Example: Find equation of motion of the following system by using Newton’s Second Law.

9. Example: Find equation of motion of the following system by using Newton’s Second Law.

10. Example: Find equation of motion of the following system by using Newton’s Second Law.

11. SOLVED DURING THE CLASS
Example: Find governing equations by a) Equivalent energy b) Newton’s Second Law by defining equivalent mass, stiffness and damping constant
SOLVED DURING THE CLASS

12. Do it yourself ! Do it yourself !
Example: Show that the system’s equation of motion is
By equivalent energy method
By Newton method
Do it yourself !
Do it yourself !