Oscillations

• Conditions for simple harmonic motion

  • acceleration towards the center
  • acceleration is proportional to displacement
• A = maximum displacement or amplitude
• Resonance - occurs when the driving frequency is equal to the natural frequency, the amplitude of oscillations drastically increase due to gaining more energy from the driving force
• Damping - when a force acts on an oscillating system and energy is lost to the environment, reducing the amplitude of oscillation
• Conservation of energy

  • At the amplitude of its oscillation the system will have the maximum potential energy
  • As it moves towards the equilibrium point, potential energy is converted to kinetic energy
• Undamped

  • No energy is lost because there are no external forces
  • Total energy of the system remains constant
• Free oscillations - occur when no external force acts on the system
• Forces oscillations - when a system experiences an external driving force which causes it to oscillate
• Light damping - the amplitude slowly decreases by a small amount each oscillation

  Critical damping - the amplitude is reduced to zero without oscillating in the shortest possible time

  Heavy damping - the amplitude reduces slower than critical damping but without oscillating
• As damping increases

  • Resonant frequency decreases
  • Maximum amplitude decreases
  • Peak of maximum amplitude becomes wider
• Ductile material - can undergo a large amount of plastic deformation before breaking. The plastic deformation of a ductile material can be used to reduce the amplitude of oscillations.