1. Day 75, Friday, 18 December, 2015 Pendulums Waves Hooke’s Law Simple Harmonic Motion Pendulums

2. Waves Type Transverse, Longitudinal, Surface Amplitude Wavelengthλ PeriodT Frequencyf = 1/T Speedv = λf

3. Waves transport energy, not mass

4. Hooke’s Law F = -kx Force with a linear restoring force Applies to springs, pendulums, marbles in bowls, ect.

5. Hooke’s law leads to Simple Harmonic Motion Simple Harmonic Motion (SHM) is the motion of a simple harmonic oscillator, a motion that is neither driven nor damped. A body in simple harmonic motion experiences a single force which is given by Hooke's law; that is, the force is directly proportional to the displacement x and points in the opposite direction.

6. Simple Harmonic Motion

7. The Pendulum

8. Forces of gravity and tension on a pendulum T cos Θ = mg

9. Pendulums have constant frequencies

10. Formula for the period of a pendulum

11. Credits http://www.sengpielaudio.com/calculator-period.htm Basic Sine Wave: http://cnx.org/content/m42242/latest/?collection=col11406/latest Simple Harmonic Motion to a Sine Wave graphic: Sine Wave Equation http://www.sengpielaudio.com/calculator-period.htm

12. Credits II Definition of Simple Harmonic Motion Wikipedia Unit Circle Graphic www.math.rutgers.edu/.../math151a/diary. html www.math.rutgers.edu/.../math151a/diary. html