Simple harmonic motion

• simple harmonic motion (SHM) is oscillating motion in which acceleration is proportional to the displacement and always in the opposite direction to the displacement
• a = -w^2x
• x = A(amplitude)cos(wt)
• an undamped pendulum will osccilate forever at the same frequency as no energy is lost
• The total energy at a certain displacement is the kinetic energy plus the potential energy at that displacement - PE+KE
• damping is the reduction in energy and oscillations due to resistive forces on the oscillating system
• critical damping is when the displacement returns to equilibrium as quick as possible ready for the next event
• heavy damping takes a long time to return to equilibrium after being displaced
• light damping causes decreases in displacement by the same fraction each time - slowly gets smaller
• Example of critical damping


  Car suspension
• example if heavy damping

  fuel gauge
• example of light damping

  air resistance
• Periodic force = force applied at regular intervals eg, pushing person on a swing
• natural frequency - the natural oscillations of a system
• when a periodic force is applied to an oscillating system it causes forced vibrations
• In SHM when the oscillations are damped their frequency does not change even though amplitude does
• Free oscillation - an oscillation where there are only internal forces acting and there is no nerdy input - oscillates at resonant frequency
• Driving frequency - the frequency of forced oscillations
• Resonance - when the frequency of the applied force to an oscillating system is equal to the systems natural f the amplitude of the resulting oscillations increases significantly
• at resonance energy is transferred from the driver to the oscillating system most efficiently the system is transferring the max KE