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MPLE HARMONIC MOTI

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DEFINITION

An object moving with simple harmonic motion oscillates up

and down or side to side.

Displacement (! is the distance o" the object "rom the

midpoint.

The RESTORING FORCE acts in the opposite direction to

displacement# towards the midpoint.

The bigger the displacement# the bigger the restoring "orce#

and it causes the object to accelerate towards the midpoint.

$o the de%nition o" $&' is WHEN ACCELERATION IS

DIRECTLY PROPORTIONAL TO THE DISPLACEMENT

ABOUT THE MIDPOINT AND IS DIRECTED TOWARDS

THE MIDPOINT.

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ENE*+, T*AN$FE*

As the object oscillates it will echange -inetic energand potential energ.

At the midpoint# -inetic energ will be highest andpotential energ lowest.

At maimum displacement (the AMPLITUDE! potentialenerg will be highest and -inetic energ lowest.

The total amount o" energ remains the same providedno eternal "orces act (eg "riction!.

A FREE OSCILLATION is one that never stops. It has nodriving "orce and is not a/ected b "riction 0 this neveractuall happens.

The RESTORING FORCE trans"ers energ between

-inetic 1 potential

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E23ATION$

I" the time starts when the object is at itsmidpoint (i.e. displacement 4 5! then #as a SINE GRAPH o" distance against time isused.

I" the time starts when the object is at eitherside o" the midpoint (i.e. maimumdisplacement! then# as a COSINE GRAPH o" against t is used.

An objects velocit is maimum when it is atthe midpoint# there"ore # as this wor-s "or asine or cosine graph o" v against t.

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+*A6&$

The velocit7time graph is the gradient o" the displacementgraph

And the displacement graph translated to the le"t b ! The acceleration7time graph is the gradient o" the velocit

graph

The velocit graph translated to the le"t b ! And the displacement graph re8ected in the " a"i#.

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DA'6IN+

Damping is the REDUCTION INAMPLITUDE o" an oscillation overtime# usuall due to energ loses to

the surroundings (e.g. "rom "riction!. The reduction in amplitude is

E$PONENTIAL.

CRITICAL DAMPING is when theamplitude is reduced to 9ero straightawa.

The graph shows %ig&t da'(ing.

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*E$ONAN:E

Occurs when the "re;uenc o" thedriving "orce E)UALS THE NATURALFRE)UENCY o" the oscillation.

It causes the AMPLITUDE OF THEOSCILLATION TO BE MA$IMUM# asthe driving "orce can trans"er the mostenerg to the object.

$hoc- absorbers act as dampers andreduce the maimum amplitude.