5.6.1. Undamped Free Vibration

Try these first

1. 1.

   What does undamped free vibration refer to?

   Hint

   Think about energy in a system that is not affected by external forces.

2. 2.

   Write down the equation of motion for undamped vibration.

   Hint

   Recall the format of differential equations.

3. 3.

   What is the equation representing undamped free vibration?

   • u¨(t) + ku(t) = 0
   • u¨(t) + ω²u(t) = 0
   • u(t) + ω²u(t) = 0

   Hint

   Recall the format of motion representing oscillations.

4. 4.

   True or False: Undamped systems will not oscillate indefinitely.

   • True
   • False

   Hint

   Consider what happens when there are no damping effects.

5. 5.

   A structure has a mass of 10 kg and a stiffness of 2000 N/m. Calculate the natural frequency. Discuss the significance of this frequency in terms of structural behavior.

   Hint

   Use the natural frequency formula to derive the answer.

6. 6.

   Discuss how undamped free vibrations might differ if damping is introduced, particularly in seismic design applications.

   Hint

   Consider energy loss effects in oscillatory systems.