6.2. Free Vibration of Undamped SDOF System

Try these first

1. 1.

   What is the governing equation for free vibration of an undamped SDOF system?

   Hint

   Think about Newton's laws applied to vibrations.

2. 2.

   What does the natural frequency indicate?

   Hint

   It is dependent on mass and stiffness.

3. 3.

   What is the equation representing free vibration of an undamped SDOF system?

   • a) mu¨(t) + ku(t) = F(t)
   • b) mu¨(t) + ku(t) = 0
   • c) mu¨(t) + c u˙(t) + ku(t) = 0

   Hint

   Remember, this involves no external forces.

4. 4.

   True or False: Free vibrations include the effect of damping.

   • True
   • False

   Hint

   Recall the assumptions for free vibration.

5. 5.

   A mass of 15 kg is attached to a spring with a stiffness of 300 N/m. Calculate the natural frequency and explain its significance in the context of an undamped SDOF system.

   Hint

   Use the natural frequency formula.

6. 6.

   If the same system experiences initial conditions of 5 cm displacement upwards and is released, describe the motion in terms of free vibrations.

   Hint

   Think about how the displacement directly relates to harmonic motion.