12.1. Concept of Two Degree of Freedom System

Try these first

1. 1.

   Define a Two Degree of Freedom system.

   Hint

   Think about how many variables are needed.

2. 2.

   What is a common example of a 2-DOF system?

   Hint

   Consider structures with multiple levels.

3. 3.

   What does a 2-DOF system require for motion description?

   • One coordinate
   • Two coordinates
   • Three coordinates

   Hint

   Recall how many factors influence the motion.

4. 4.

   True or False: A two-story building is an example of a 2-DOF system.

   • True
   • False

   Hint

   Think about how buildings respond to forces.

5. 5.

   Given a 2-DOF system defined by masses m1 = 1500kg, m2 = 2000kg, and stiffness k1 = 30000N/m, k2 = 25000N/m, k12 = 5000N/m. Derive the equations of motion.

   Hint

   Recall how to express dynamics through mass and stiffness matrices.

6. 6.

   A 2-DOF system has two natural frequencies of 5Hz and 7Hz. What will be the effect on resonance if the system is excited near these frequencies?

   Hint

   Think about how objects resonate and the importance of matching frequencies.