1. Unit 4: Sound and Waves

2.  Seeing a pattern of cycles on a graph is an indication that harmonic motion is present  Periodic motion: graphs repeat every period (from crest to crest)  Amplitude on a graph  Distance between highest and lowest points  Period of a graph  Time difference between the beginning of the cycle and the end

3. CIRCLES AND HARMONIC MOTION  Cycles of circular motion always have a length of 360 degrees  Phase: where the oscillator is in its cycle 11.3 SIMPLE MECHANICAL OSCILLATORS  Pendulum  Force that always pulls the pendulum back to the center comes from its weight  Spring  Springs of a car are compressed and extended in rhythmic patterns  String  Such as a guitar string, it will vibrate and make waves

4.  Katherine Johnson  Born in 1918  Hired as a mathematician by a government agency that became NASA  Determined trajectories for manned and unmanned spacecraft ▪ Helped plan the Apollo missions and developed their emergency navigation system