6.3. Free Vibration of Damped SDOF System

Try these first

1. 1.

   What is the governing equation of motion for a damped SDOF system?

   Hint

   Think about the forces acting on the mass.

2. 2.

   Define the damping ratio.

   Hint

   It’s a ratio that relates damping to mass and stiffness.

3. 3.

   What type of damping occurs when ζ < 1?

   • Critically damped
   • Underdamped
   • Overdamped

   Hint

   Remember the range of the damping ratio.

4. 4.

   True or False: A critically damped system oscillates.

   • True
   • False

   Hint

   Think about the speed of equilibrium.

5. 5.

   Design a damped SDOF system for a building with a mass of 5000 kg, and a stiffness of 200000 N/m that experiences a damping ratio of 0.05. Calculate the necessary damping coefficient.

   Hint

   You have the required mass and stiffness values, ensure you correctly apply the formula.

6. 6.

   Explain how the characteristics of the earthquake ground motion could influence the damping response of a structure.

   Hint

   Consider how different earthquakes have varying characteristics.