Further Mechanics

• Angular Speed: Rate of change of angular displacement with respect to time
• Centripetal Acceleration: Acceleration of an object towards the centre of a circle when it is in motion travelling at a constant speed
• Centripetal Force: Resultant force towards the centre of a circle required to keep an object in uniform circular motion
• Conditions for SHM:

  • Acceleration is proportional to displacement
  • Acceleration acts in opposite direction to displacment
• Damping: Reduction in energy and amplitude of oscillations due to external resistive forces acting on the system
• Light Damping: Amplitude decreases exponentially with time and energy decreases by small amounts after each oscillation
• Critical Damping: System will return to equilibrium with no oscillations - lots of energy is released
• Heavy Damping: System will take a long time to return to equilibrium without oscillating
• Free Oscillation: An oscillation where there are no external forces applied to the system - oscillates at its resonant frequency
• Forced Oscillations: An oscillation acted on by a periodic external force where energy is given into the system to sustain oscillations
• Resonance: When the frequency of the periodic force is equal to the natural frequency of the system, a lot of energy is gained resulting in a rapidly increasing amplitude.