-Simple Pendulum-Simple Pendulum-Physical Pendulum-Physical Pendulum-Torsional Pendulum-Torsional Pendulum

AP Physics CMrs. Coyle

http://article.wn.com/view/2010/08/22/Crystal_Mountain_will_feature_new_gondola_terrain_park/

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