7.3. Equation of Motion for Free Vibration

Try these first

1. 1.

   What does m represent in the equation of motion?

   Hint

   Think about what you are trying to model in a physical system.

2. 2.

   What is the relationship between mass and natural frequency?

   Hint

   Consider how heavy objects move compared to lighter ones.

3. 3.

   What is the equation of motion for an undamped SDOF system?

   • mx¨(t) + kx(t) = 0
   • mx¨(t) - kx(t) = 0
   • kx(t) = 0

   Hint

   Remember, it describes mass and stiffness acting on displacement.

4. 4.

   True or False: Increasing mass will increase the natural frequency of a system.

   • True
   • False

   Hint

   Think about how heavier masses respond compared to lighter ones.

5. 5.

   A system has a mass of 10 kg and a spring constant of 400 N/m. Calculate the natural frequency and time period.

   Hint

   Use the respective formulas for ω and T.

6. 6.

   If the damping coefficient is introduced into the equation mx¨(t) + cx˙(t) + kx(t) = 0, describe how it changes the dynamic response.

   Hint

   Think about what happens when friction is introduced to the system.