9.2. Equation of Motion for Single Degree of Freedom (SDOF) System

Try these first

1. 1.

   What does 'm' represent in the equation of motion?

   Hint

   Think about what quantity needs to be multiplied by acceleration.

2. 2.

   What is the role of the damping coefficient?

   Hint

   Consider how the energy dissipates in vibrating systems.

3. 3.

   What does 'c' in the equation of motion refer to?

   • Mass
   • Damping Coefficient
   • Stiffness

   Hint

   Think about how systems return to rest.

4. 4.

   True or False: The impulse response function can help predict the behavior of structures during an earthquake.

   • True
   • False

   Hint

   Remember the importance of analyzing dynamic responses.

5. 5.

   Given the mass m=2kg, damping c=3N·s/m, and stiffness k=15N/m, derive the equations of motion and impulse response for this SDOF system.

   Hint

   Start by substituting the values into the motion equation.

6. 6.

   If the damped natural frequency is ωd = 5 rad/s, what does that say about the damping ratio in your impulse response?

   Hint

   Connect the natural frequency and the damping ratio for analysis.