6.4.1. Equation of Motion for External Force

Try these first

1. 1.

   What is the equation of motion for an SDOF system under an external force?

   Hint

   Refer to the key equation discussed.

2. 2.

   List the three components of an SDOF system.

   Hint

   Remember the MCD acronym.

3. 3.

   What does F(t) represent in the equation of motion?

   • Inertia
   • External Force
   • Damping Coefficient

   Hint

   Think about what force is applied externally.

4. 4.

   True or False: The equation of motion can be solved using Laplace Transforms.

   • True
   • False

   Hint

   Consider the advantages of transforming differential equations.

5. 5.

   Consider a building modeled as an SDOF system with a mass of 500 kg, a damping coefficient of 100 N.s/m, and stiffness of 2000 N/m. An external force of 300 N is applied. Write the equation of motion and solve for the response under this force using the methods discussed.

   Hint

   Start by inserting the values into the equation to observe motion.

6. 6.

   Discuss how the equation of motion would change if the damping coefficient is increased significantly. What would this imply for the system's response?

   Hint

   Consider the relationship between damping and oscillation behavior.