11.3. Mode Shapes and Natural Frequencies

Try these first

1. 1.

   Define natural frequency in your own words.

   Hint

   Think about how tuning forks resonate.

2. 2.

   What are mode shapes?

   Hint

   Consider how different instruments vibrate.

3. 3.

   What defines the natural frequencies of a system?

   • Mass and damping
   • Mass and stiffness
   • Shape and load

   Hint

   Consider what properties influence oscillation.

4. 4.

   True or False: Mode shapes can interfere with each other.

   • True
   • False

   Hint

   Think about independence in terms of vectors.

5. 5.

   Given a two-mass spring system, derive the natural frequencies and mode shapes of the system. Consider both masses and springs in your analysis.

   Hint

   Make use of the symmetry in the eigenvalue problem.

6. 6.

   In a multi-storey building, discuss how mode shapes affect the building's response to seismic activity, providing specific examples.

   Hint

   Consider how the distribution of mass can modify the force spread during an earthquake.