1. WEEK-3: Free Vibration of SDOF systems
Assoc. Prof. Dr. Abdullah Seçgin

2. Free vibration of SDOF systems
Assume following initial conditions
Natural frequency
Damping Ratio
Equation of motion
Standart form of equation of motion
Assume a harmonic solution

3. Free vibration of SDOF systems
Equation of motion
Harmonic solution
Types of Free Vibrations

4. Free vibration of SDOF systems
General harmonic solution
Applying initial conditions

5. Example:

6. Example:

7. 1.Underdamped vibration
By applying initial conditions and expand with cos and sine terms gives

8. 1.Underdamped vibration

9. 1.Underdamped vibration

10. Example: Governing equation of motion of an underdamped single degree of freedom system is given as
Find the natural frequency
Find the damping ratio
Find the damped natural frequency of the system
Find the free vibration response amplitude
and its phase for the following initial conditions:
e) Draw roughly the amplitude-time graphics of the response

11. Example: Governing equation of motion of an underdamped single degree of freedom system shown below is given as
Find all vibration parameters

12. Solution: