7.7. Graphical Representation of Motion

Try these first

1. 1.

   Define displacement in the context of an SDOF system.

   Hint

   Think about how far the mass moves from its rest position.

2. 2.

   What shape does the displacement-time graph of an undamped system have?

   Hint

   Visualize how waves move up and down continuously.

3. 3.

   What type of motion is exhibited by an undamped SDOF system?

   • Random
   • Sinusoidal
   • Linear

   Hint

   Think about the shape of waves in motion.

4. 4.

   True or False: The amplitude of an undamped SDOF system decreases over time.

   • True
   • False

   Hint

   Consider the absence of energy loss.

5. 5.

   For a mass-spring system with a mass of 2 kg and a spring constant of 50 N/m, calculate the natural frequency and sketch the corresponding displacement versus time graph.

   Hint

   Remember the formula for natural frequency and how to sketch oscillatory functions.

6. 6.

   Explain how changes in mass would affect the phase diagram of a vibrating system and what it implies about the velocity at maximum displacement.

   Hint

   Think about how mass influences both shape and speed of oscillation in a dynamic system.