-Simple Pendulum -Physical Pendulum -Torsional Pendulum AP Physics C Mrs. Coyle

The Simple Pendulum The motion of a simple pendulum is very close to a SHM oscillator, i f the angle is <10 o

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 ω 2 =g/L

Period of the Simple Pendulum  =  max cos (t + ) Angular frequency: Period:

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 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

Period 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:

Torsional Pendulum Restoring torque α  is the torsion constant of the wire

Period of Torsional Pendulum Angular frequency: Period: