7.6. Initial Conditions and System Response

Try these first

1. 1.

   What is meant by initial displacement in an SDOF system?

   Hint

   Think about the position relative to the resting state.

2. 2.

   How does initial velocity differ from initial displacement?

   Hint

   Consider it as the speed or rate of change of position.

3. 3.

   What does the initial displacement x(0) represent in an SDOF system?

   • Position at t=0
   • Final position
   • Velocity at t=0

   Hint

   Think about the starting point of oscillation.

4. 4.

   True or False: Initial velocity has no effect on the amplitude of the vibration.

   • True
   • False

   Hint

   Consider how speed at the start influences oscillation.

5. 5.

   A block on a spring has an initial displacement of 2 m and is released with an initial velocity of 5 m/s. Find the equation for its motion and explain each component.

   Hint

   Use the formula involving initial conditions to build the motion equation.

6. 6.

   If the initial conditions of a system are altered such that the displacement is halved, but velocity doubles, derive the new equation of motion.

   Hint

   Translate altered conditions into the motion equation format.