-Simple Pendulum -Physical Pendulum - Torsional Pendulum
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Transcript of -Simple Pendulum -Physical Pendulum - Torsional Pendulum
-Simple Pendulum-Simple Pendulum-Physical Pendulum-Physical Pendulum-Torsional Pendulum-Torsional Pendulum
AP Physics CMrs. Coyle
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The Simple PendulumThe Simple Pendulum
The motion of a simple pendulum is very close to a SHM oscillator, if the angle is <10o
The tangential component of mg is the restoring force
s=Lsin
For small values of sin
Since α is proportional to this motion is SHM and let ω2=g/L
2
2sint
d sF mg m
dt
2
2sin
d g g
dt L L
Period of the Simple Period of the Simple PendulumPendulum
= max cos (t + )
Angular frequency:
Period:
g
L
22
LT
g
Question: If a pendulum was taken to a planet where the acceleration due to gravity was four times that of g on the earth, how would the period change?
Physical PendulumPhysical Pendulum
An object that oscillates about a fixed axis (not through its center of mass) and the object cannot be approximated as a particle.
Torque = Iα
For small angles sinθ=θ
2
2sin
dmgd I
dt
22
2
d mgd
dt I
Period of the Physical PendulumPeriod of the Physical Pendulum
Since α is proportional to θ the motion has the form of an object in simple harmonic motion.
Angular frequency:
Period:
mgd
I
22
IT
mgd
Torsional PendulumTorsional Pendulum
Restoring torque α
is the torsion constant of the wire
2
2
2
2
dIdt
d
dt I
Period of Torsional PendulumPeriod of Torsional Pendulum
Angular frequency:
Period:
I
2I
T