Simple Harmonic Motion and Wave Interactions Physics – Chapter 12-1, 12-2 Simple Harmonic Motion and Wave Interactions

Wave Interactions (12-1) Simple Harmonic Motion A. Hooke’s law - Periodic motion – a repeated motion example: swinging on a swing, grandfather clock pendulum, mass on a spring

 When a spring with a mass is stretched or compressed and released the energy is also released and the spring-mass system vibrates back and forth in a periodic manner

Velocity is maximum at equilibrium position (x=0) Spring force and acceleration reach their maximum at max displacement (x = 1 or x = -1)

In the absence of friction (damping) the mass-spring system would oscillate forever The spring force pulls or pushes the mass toward equilibrium  The restoring force

If the restoring force is proportional to the displacement then the motion is called simple harmonic motion - Simple Harmonic Motion – vibration around an equilibrium position where restoring force is proportional to displacement  will go back and forth over the same path

Hooke’s Law Felastic = -k•x x = displacement  measured in meters k = spring constant  measured in Newtons/meter F = spring force (elastic)  measured in Newtons

The negative sign shows that the spring force is opposite in direction to the mass’ displacement and moves it towards equilibrium This applies to a mass vibrating horizontally If vibrating vertically, you must take gravity into account ( kx = -mg) The system has elastic potential energy, which changes to kinetic and back again.

B. Simple Pendulums - A mass (called a pendulum bob) attached to a fixed string with negligible mass - Can be approximated to a physical pendulum

12-2 Measuring Simple Harmonic Motion Simple harmonic motion – Vibration around an equilibrium point, in which displacement force = force pushing it back toward equilibrium

Amplitude – maximum displacement from equilibrium Period (T) – time it takes for one full cycle of motion to occur  measured in seconds (s) Frequency (f) – number of cycles (vibrations) per second  measured in Hertz (Hz)   1 Hertz = 1 cycle / second

* Period and frequency both involve time f = 1/T --- T = 1/f  Inversely related * If you have one of the values, the other can always be calculated

Simple Pendulum  Period depends on the string length and free-fall acceleration *For small angles (<15o), amplitude and mass are not factors in a pendulum’s period  

*Equations for pendulum and mass-spring system*