definitions and concepts

• angular speed

  a measure of the speed of an object's angular rotation

  • equal to the frequency of rotation multiplied by $2\pi$
• centripetal acceleration

  the acceleration of an object moving in circular motion

  • any object in circular motion must have an acceleration since the direction of the object, and therefore the velocity of the object, is constantly changing
• centripetal force

  the resultant force responsible for an object moving in circular motion

  • centripetal forces always act towards the centre of the object's rotation
• critical damping

  the form of damping that reduces the displacement of an oscillating object to its equilibrium position in the quickest time possible and without further oscillation
• damping

  the dissipation of energy from an oscillating system

  • the consequence is that the amplitude of oscillation will decrease
  • damping occurs when a force opposes the system's motion
• forced vibration

  repeated up and down oscillations at the frequency of the driver

  • the amplitude of oscillation is small at high frequencies and large at low frequencies
• free vibrations

  oscillations that are not caused by a driver

  • an object will naturally oscillate at its natural frequency
• overdamping

  a type of damping where the system is damped more than required to stop the oscillations

  • it takes longer for the system to return to equilibrium than for critical damping
• radian

  a unit of angle
• resonance

  resonance occurs when the frequency of oscillations is equal to the natural frequency of the oscillating system

  • the rate of energy transfer is at a maximum during resonance
• simple harmonic motion

  motion where the acceleration of an object is directly proportional, and in the opposite direction, to its displacement
• underdamping

  a type of damping where energy is gradually removed from the system and the amplitude of oscillations slowly decrease