6.1 - Further Mechanics

• What kind of force is required to keep an object moving in a circle at a constant speed?

  A constant centripetal force (a resultant force acting towards the centre of the circle)
• What is a radian?

  The angle of a circle sector such that the radius is equal to the arc length
• What are the conditions for SHM?

  - Acceleration must be directly proportional to displacement and in the opposite direction:

  (a ∝ -𝑥)

  - It must act towards equilibrium
• Define free vibrations


  The frequency a system tends to vibrate at in a free vibration is called the natural frequency
• Define forced vibrations


  A driving force causes the system to vibrate at a different frequency. For higher driving frequencies, the phase difference between the driver and the oscillations rises to π radians. For lower frequencies, the oscillations are in phase with the driving force. When resonance occurs, which is when it most efficiently transfers energy to the system, the phase difference will be π/2 radians.
• Define damping and explain what is critical damping, overdamping and underdamping

  Damping occurs when an opposing force dissipates energy to the surroundings

  Critical damping reduces the amplitude to 0 in the quickest time

  Overdamping is when the damping force is too strong and it returns to equilibrium slowly without oscillation

  Underdamping is when the damping force is too weak and it oscillates with exponentially decreasing altitude
• What happens to a vibration with greater damping?

  For a vibration with greater damping, the amplitude is lower at all frequencies due to greater energy losses from the system. The resonant peak is also broader because of the damping.
• What are some implications of resonance with real life?

  Implications of resonance include that soldiers must break stop when crossing bridges and vehicles must be designed so that there are no unwanted vibrations