10.2.1. Underdamped Case (ζ<1)

Try these first

1. 1.

   Define the damping ratio.

   Hint

   Think about how quickly the system stops moving.

2. 2.

   What is the formula for the damped natural frequency?

   Hint

   Consider the relationship between the natural frequency and damping.

3. 3.

   What is characterized by a damping ratio less than 1?

   • Overdamped System
   • Critically Damped System
   • Underdamped System

   Hint

   Remember what happens when the damping ratio is low.

4. 4.

   True or False: The impulse response function can predict behavior for all systems including nonlinear systems.

   • True
   • False

   Hint

   Think about the properties of linear versus nonlinear systems.

5. 5.

   Calculate the damped natural frequency for a system with a natural frequency of 5 Hz and a damping ratio of 0.3.

   Hint

   Use the formula ω_d = ω_n √(1 - ζ²).

6. 6.

   Explain how increasing the damping ratio would affect the oscillations of a structure during an earthquake.

   Hint

   Consider the balance between oscillation and damping energy.