Damped Harmonic Motion
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Damping
ð Damping is any effect that tends to reduce the amplitude of oscillations in an oscillatory system It is the process of energy loss
ð The amplitude of any real oscillating system will slowly decrease over time and eventually stop due to Ø air resistance Ø internal friction
ð This is referred to as damped harmonic motion
ð The decrease in amplitude is shown by the dotted lines
ð But, if the damping is not large we can treat them as SHM - a much simpler problem |
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Non SHM
ð There are 3 situations in which the motion no longer resenbles SHM
Ø Under damped: System makes several swings before coming to rest - curve A More heavily damped version of the above figure
Ø Critically damped: System reaches equilibrium in shortest time - curve B Door closing sytems and car shocks when new - deteriorate to under damped as they age A gun is another example - return to firing position in shortest amount of time after firing
Ø Over damped: Damping is so large it takes a long time to reach equilibrium - curve C |
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Overdamped Systems
T is the period (previous discussion): the time required to complete one cycle
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Underdamped Spring-Mass System How would it behave if it were Overdamped? Critically Damped? |
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