14.2.2. Undamped Natural Frequency

Try these first

1. 1.

   What is the formula for undamped natural frequency?

   Hint

   Look for the relationship between stiffness and mass.

2. 2.

   What happens to the natural frequency when mass is increased?

   Hint

   Think about the formula and how mass is positioned.

3. 3.

   What does the undamped natural frequency represent?

   • Vibrations with external damping
   • The natural frequency when a system oscillates freely
   • A measure of mass only

   Hint

   Think about conditions without external forces.

4. 4.

   True or False: Increasing mass decreases the undamped natural frequency.

   • True
   • False

   Hint

   Consider how mass impacts the frequency derived from the formula.

5. 5.

   A building has a natural frequency of 2 rad/s. If the stiffness is changed to 800 N/m while maintaining the mass, what new natural frequency will be calculated?

   Hint

   Use the formula to relate stiffness, mass, and frequency.

6. 6.

   Discuss how varying environmental factors (like soil conditions) might affect a structure's undamped natural frequency.

   Hint

   Consider the impact of flexibility or rigidity from the surrounding environment.