Simple Harmonic Motion

• In Simple Harmonic Motion

  The acceleration is proportional to the displacement

  The acceleration is always directed towards the equilibrium position

  This can be related to the equation:

  a = -W^2 *x

  negative as the acceleration is directed towards the equilibrium position
• Acceleration graph is:

  A straight line through the origin

  negative gradient: as acceleration is towards the equilibrium

  Gradient = -W^2

  can be put in the equation 2*pi*F or 2 pi/T
• Calculations for Displacement, x:

  x = A cos(w*t) - which is to be used when the oscillator is at the maximum amplitude

  x - A sin(w*t) - which is used when the oscillator is at equilibrium
• Resonance occurs when the driving frequency matches the natural frequency

  Amplitude increases considerably
• Natural Frequency is the frequency at which an object will oscillate after initial disturbance
• Natural frequency with damping

  Amplitude decreases

  The peak occurs at a lower frequency and curve appears to shift to the left

  
• Resonance Examples:

  Microwave oven:

  The driving frequency of EM waves matches the natural frequency of the water molecules therefore resonance occurs and this increases amplitude and the kinetic energy of the water molecules

  Oscillating bridge:

  The driving frequency of the wind matches the natural frequency of the bridge therefore resonance occurs this increases the amplitude of the vibrations of the bridge