1.5. Forced Vibration of SDOF Systems

Try these first

1. 1.

   Define forced vibration in the context of SDOF systems.

   Hint

   Think about what causes the vibrations in terms of external stimuli.

2. 2.

   What is the transient response?

   Hint

   Consider how the system behaves immediately versus later.

3. 3.

   What occurs during forced vibration?

   • Only due to initial disturbance
   • Due to continuous external force
   • Only in free conditions

   Hint

   Consider the definition difference between free and forced vibrations.

4. 4.

   True or False: Steady-state response only occurs in the absence of damping.

   • True
   • False

   Hint

   Remember, all systems experience steady behaviors with continuous forces.

5. 5.

   Calculate the steady-state amplitude for a SDOF system with mass = 5 kg, stiffness = 500 N/m and damping = 40 Ns/m given an external force F_0 = 200 N at frequency ω = 5 rad/s.

   Hint

   Break down the formula into components step by step.

6. 6.

   Discuss the implication of resonance in seismic design. Why is ensuring that natural frequencies are distinct from seismic excitation frequencies crucial?

   Hint

   Reflect on the consequences of structural overload during actual seismic events.