Damped oscillations

1
Damped oscillations

• Objective
• (k) describe the effects of damping on an
  oscillatory system

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Outcomes

• ALL MUST
• Be able to define damping.
• Be able to understand where damping may occur.
• Be able to understand what an exponential
  relationship is.
• MOST SHOULD
• Be able to describe an investigation where
  damping is caused (i) by the drag of the air and
  (ii) by eddy currents (electromagnetic damping).
• To show that for light damping, the amplitude of
  oscillations decays exponentially with time.

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The Velocipede

• Or Boneshaker from the 1860s
• Its adjustable wooden seat has no springs under
  it hence it was known as a "boneshaker". Lacking
  the comforts of the modern bicycle, it has been
  relegated to the museum.

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Penny Farthing

• Rubber wheels made this more comfortable for a
  while

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The Pneumatic-Tyre

• From the 1890s air was used is the tyres for
  added comfort

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Suspension Bikes

• Suspension is used now on bikes especially
  those that are designed to go off road

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Suspension

• Spring suspension is made up of two parts
• A spring
• And a shock absorber or Damper
• Why?

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Suspension

• Springs are good at absorbing energy
• But not so good at dissipating it
• You want to absorb an impact
• But then dont want the spring to keep bouncing
• The oscillations must be damped

9
Dampers (Shock absorbers)

• Using oil (a viscous fluid)
• Which is a sticky substance that objects cant
  move through easily
• Here, the spring takes the shock and then its
  oscillations are slowed with oil

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Other examples

• Compressed air shocks
• Spring shocks a pair of springs working against
  each other
• Electromagnetic damping using a magnetic field
  to slow oscillations (used in Galvonometers)
• The paper cone of a loud speaker vibrates but is
  heavily damped as it transforms its kinetic
  energy into sound energy in the surrounding air

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Oscillations and damping

• In S.H.M, (i) the period is independent of the
  amplitude and (ii) the total energy remains
  constant
• In practise many objects only undergo approximate
  s.h.m because (i) the restoring force is not
  exactly proportional to the displacement and (ii)
  resisting forces oppose the motion (e.g. air
  resistance)

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Amplitude of damped oscillations

• Light
• Critical
• Heavy

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Light
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Critical