5.3 - Oscillations

• Amplitude

  Max displacement from the equilibrium position
• Damping

  Work done by the resistive forces to reduce the amplitude of vibration and Ek
• Equation for acceleration using SHM graph

  w²Acoswt
• Equation for displacement using SHM graph

  -Acoswt
• Equation for velocity using SHM graph

  wAsinwt
• Forced vibration

  When a driver forces an object to vibrate at a frequency other than its natural frequency
• Natural frequency

  Frequency of vibration of a free moving object undergoing shm
• Problem with resonance

  Wind causes bridges to resonate Wind is the driver Bridges is being driven
• Problem with resonance

  Wind causes bridges to resonate Wind is the driver Bridges is being driven
• Resonance

  When the energy of an oscillator, driven at its natural frequency, increases (amplitude also increases)
• SHM conditions

  Acceleration is proportional to displacement from equilibrium Acceleration acts towards equilibrium
• Simple harmonic motion

  Oscillating objects with acceleration towards the equilibrium position, that is proportional to the displacement from it
• Useful application of resonance

  Cooking: microwaves cause water molecules to resonate Microwaves are the driver Water molecules are being driven
• When does resonance occur

  When driving frequency matches natural frequency
• Resonance energy graph

  Kinetic energy max at 0 displacement

  Potential energy max at amplitude

  
• Equation for Time independent from gravity

  Where k is the spring constant

  
• Equation for Time independent from mass

  Where L is the length

  
• Light damping

  Occurs naturally and the Amplitude decreases exponentially

  Eg pendulum in air
• Heavy damping

  Amplitude decreases dramatically

  Eg pendulum in water
• Critical damping

  Object stops before one oscillation is complete

  Eg pendulum in treacle