10.1. Equation of Motion for Linear SDOF System

Try these first

1. 1.

   What does the 'm' stand for in the equation of motion?

   Hint

   Think about what affects inertia.

2. 2.

   Define damping in the context of SDOF systems.

   Hint

   Recall how oscillations behave over time.

3. 3.

   What does the equation mx¨(t) + cx˙(t) + kx(t) = F(t) represent?

   • A thermal equation
   • An equation of motion for a linear SDOF system
   • A static equilibrium condition

   Hint

   Remember, we are discussing motion dynamics.

4. 4.

   True or False: Stiffness determines how quickly a system can return to equilibrium after deformation.

   • True
   • False

   Hint

   Consider what happens after a force is removed.

5. 5.

   Consider an SDOF system where mass m is 10 kg, damping coefficient c is 5 Ns/m, and stiffness k is 100 N/m. Calculate the natural frequency of the system.

   Hint

   Use the formula for natural frequency and plug in the given values.

6. 6.

   Discuss the differences in the equation of motion between an underdamped and overdamped system and calculate the respective damping ratios if m=1 kg, c=0.5 Ns/m for the underdamped case, and c=2 Ns/m for the overdamped case with k=4 N/m.

   Hint

   Remember that ζ < 1 denotes underdamping and ζ > 1 denotes overdamping.