1. November 22, 2005 Physical Pendulum Pivot disk about a point a distance h from the center; What is the period T of oscillation? h mg   Find  (t) for this oscillatory motion. Pivot point Radius r Parallel axis theorem Same period of oscillation ! Torque from mg is restoring force 2 nd order differential equation Solution “Angular frequency” 

2. November 22, 2005 Relation between Simple Harmonic Motion and Uniform Circular Motion x y r  Let  = constant so that  (t) =  t, i.e. particle rotates around circle with constant speed. At a given , the y coordinate of the particle is: Like a mass oscillating on a vertical spring, the “projection” of uniform circular motion on one axis exhibits simple harmonic motion. x y Follow y coordinate as a function of time as object rotates around circle 

3. November 22, 2005 Standing Waves on Stringed Instruments The string length (distance from finger to bridge) determines the wavelength of standing waves on the string. EFFECT EXPLANATION 1.Placing finger on string raises pitch 2. Tune string higher, i.e. increase tension, raises pitch 3.Compare pitch of different strings, observe lower strings are heavier Constant Finger shortens So f increases T increases, with constant So f increases  increases for thicker strings, with constant So f decreases for thicker strings