11. Multiple Degree of Freedom (MDOF) System

Try these first

1. 1.

   What is a Degree of Freedom (DOF)?

   Hint

   Think about how many independent movements are needed for a system.

2. 2.

   Name a common example of an MDOF system.

   Hint

   Consider structures that have multiple parts.

3. 3.

   What defines a multiple degree of freedom (MDOF) system?

   • Only one independent motion
   • More than one independent coordinate
   • No independent motion

   Hint

   Think about structures that can vibrate in different ways.

4. 4.

   True or False: The mass matrix in an MDOF system is typically non-diagonal.

   • True
   • False

   Hint

   Consider how mass is distributed across a structure.

5. 5.

   A 3-story building can be modeled as an MDOF system. Each floor has a mass of 1000 kg, and the stiffness varies with floor height. Formulate the equations of motion.

   Hint

   Consider how the mass of the floors contributes to the overall mass matrix.

6. 6.

   How would you approach calculating the natural frequencies of a damped MDOF system? Include steps.

   Hint

   Remember that damping alters the response characteristics.