SHM

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define SHM
Simple harmonic motion occurs when the force on an object is proportional and in the opposite direction to the displacement of the object. (F=-kx) I.e the more you pull it one way the more it wants to move the other.
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point of max V on a swing
eqbm position (in middle of cycle)
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point of max acceleration on swing
at both extremes
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acceleraiton is proportional to
displacement
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displacement equation SHM
x = Asinωt
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Velocity equation SHM
v = Aωcosωt
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acceleration equation SHM
a = -A(ω^2)sinωt
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Since a is directly proportional to x give equation
a = -x(2πf)^2 (-ve since always opposes displacement)
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v=
±2πf(A^2 - x^2)^0.5
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Vmax at x = 0 is therefore
±2πfA
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period of a simple pendulum
T = 2π (l/g)^0.5
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period of mass on a spring
T = 2π (m/k)^0.5
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define damping
a reduction in the amplitude of an oscillation as a result of energy loss in the system (e.g air resistance or on purpose)
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to get to eqbm position quickly we use
critical damping
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if we damp even more...
it will take a long time to reach eqbm (overdamping)
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what is resonance
when a driving frequency is equal to the natural frequency, the amplitude of oscillation will build and build (there will be MAXIMUM energy transfer)
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how do we reduce effect of resonance
use damping
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what material is best for soundproofing:
porous material/made up of small fibres
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why do springs/dampers reduce vibrations
spring deforms (instead of object), absorbing energy
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energy is proportional to
amplitude squared
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Definition of free oscillation.
the oscillation of a body or system with its own natural frequency and under no external influence other than the impulse that initiated the motion
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Other cards in this set

Card 2

Front

point of max V on a swing

Back

eqbm position (in middle of cycle)

Card 3

Front

point of max acceleration on swing

Back

Preview of the front of card 3

Card 4

Front

acceleraiton is proportional to

Back

Preview of the front of card 4

Card 5

Front

displacement equation SHM

Back

Preview of the front of card 5
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