11.2. Equations of Motion for Undamped MDOF System

Try these first

1. 1.

   What does MDOF stand for?

   Hint

   Think about the number of independent motions in a system.

2. 2.

   What is the primary equation governing undamped MDOF systems?

   Hint

   This equation shows the relationship between mass, stiffness, and acceleration.

3. 3.

   What does MDOF stand for?

   • Single Degree of Freedom
   • Multiple Degrees of Freedom
   • Multiple Dynamic Oscillators

   Hint

   Consider the definition involving motion descriptions.

4. 4.

   The mass matrix in an MDOF system is usually:

   • True
   • False

   Hint

   Reflect on the independence of movement across different degrees of freedom.

5. 5.

   Given a three-story building as an MDOF system, with each floor having different lumped masses, formulate the equations of motion for the system. Specify the mass and stiffness matrices.

   Hint

   Remember, the mass matrix for lumped systems is diagonal, while the stiffness matrix will depend on how the springs are distributed.

6. 6.

   How does the change in one mass in a multi-storey MDOF building affect its overall behavior during seismic activity?

   Hint

   Think about how balance and distribution of weight impact stability.