# Waves - Tenafly Public Schools -Simple Pendulum -Physical Pendulum -Torsional Pendulum AP Physics C Mrs. Coyle http://article.wn.com/view/2010/08/22/Crystal_Mountain_will_feature_new_gondola_terrain_park/ The motion of a simple pendulum is very close to a SHM oscillator, if the angle is <10o The Simple Pendulum

The tangential component of mg is the restoring force 2 s=Lsin For d s Ft mg sin m 2 dt small values of sin d 2 g g sin

2 dt L L Since is proportional to this motion is SHM and let 2=g/Lg/L =g/L max cos (t + ) Angular Period: frequency: g L

2 L T 2 g Period of the Simple Pendulum 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? An

object that oscillates about a fixed axis (not through its center of mass) and the object cannot be approximated as a particle. Torque =g/L I 2 d mgd sin I 2 dt For small angles sin=g/L 2 d

mgd 2 2 dt I Physical Pendulum Since is proportional to the motion has the form of an object in simple harmonic motion. Angular Period:

frequency: mgd I 2 I T 2 mgd Period of the Physical Pendulum Restoring torque

is the torsion constant of the wire 2 d I 2 dt 2 d 2 dt I Torsional Pendulum Angular

Period: frequency: I I T 2 Period of Torsional Pendulum