16.3.2. Equations of Motion

Try these first

1. 1.

   What does the mass matrix [M] represent?

   Hint

   Think about what physical property the matrix relates to.

2. 2.

   What is the significance of external force vector {f(t)}?

   Hint

   Remember how these forces influence movement.

3. 3.

   What is the correct equation for an undamped MDOF system?

   • [M]{u¨(t)} + [C]{u˙(t)} + [K]{u(t)} = {f(t)}
   • [M]{u¨(t)} + [K]{u(t)} = {f(t)}
   • [C]{u˙(t)} + [K]{u(t)} = {f(t)}

   Hint

   Focus on the absence of the damping term.

4. 4.

   True or False: The damping matrix [C] is included only in damped MDOF systems.

   • True
   • False

   Hint

   Think about the effects of damping.

5. 5.

   Consider a two-degree-of-freedom MDOF system with mass matrix [M] = [2 0; 0 3] and stiffness matrix [K] = [4 -2; -2 3]. Derive the equation of motion for this system.

   Hint

   Use the definition of MDOF systems and substitute the matrices.

6. 6.

   An MDOF system has an undamped response. How would you adjust the equation to account for damping, and what implications might that have?

   Hint

   Consider how energy dissipation modifies overall response.