Happy Thursday! Get ready for warm up #9 Warm ups are due tomorrow! Get ready to take notes: we are starting on a new unit!! REP: 2007-Nov-28SHM1

Warm up # 8 REP: 2007-Nov-28SHM2

Simple Harmonic Motion “back & forth”

REP: 2007-Nov-28SHM4 Simple Harmonic Motion (SHM) simple harmonic motion – Simple harmonic motion (SHM) is a repeated motion of a particular frequency and period Happens in spring, pendulums and waves Occurs when the restoring force on an object is directly proportional to the displacement of the object from its equilibrium position Restoring force  brings an object back to its equilibrium position

200 grams Vibrating Tuning fork A mass on a spring A boy on a swing

REP: 2007-Nov-28SHM6 T= period of time L= length of pendulum g = acceleration due to gravity

FORMULA FOR THE PERIOD OF A A SPRING REP: 2007-Nov-28SHM7 Period of spring oscillation where m = mass k = spring constant The “spring Constant” is the strength of the spring Unit is N/m or Newton/meter

The period of oscillation of a spring Depends upon two things: 1.The mass 2.The strength of the spring (k) REP: 2007-Nov-28SHM8

REP: 2007-Nov-28SHM9 Small masses vibrate with shorter periods Large masses vibrate with longer periods Springs with larger constants (stronger) vibrate with shorter periods Springs with smaller constants (weaker) vibrate with longer periods

Spring Oscillation You can determine the strength of a spring, the amount of mass and the displacement of a spring by using Hooke’s Law SHM10 Hooke’s Law where x =  length k  spring constant

A butcher prepares cuts of meat daily. He places a 2.2 kg package on his scale, which compresses the scale by 2.8 cm. What is the spring constant of his scale? REP: 2007-Nov-28SHM11

REP: 2007-Nov-28SHM12 SHM: Period & Frequency Period ( T ) [measured in seconds]  The time it takes for one complete oscillation (e.g., back-and-forth) Frequency ( f ) [measured in hertz (Hz)]  The number of oscillations that occur in one second or Hz = sec -1 = 1 sec Period & frequency are reciprocals (inverses) of each other

REP: 2007-Nov-28SHM13 SHM: Pendulum Pendulums display simple harmonic motion if the angle of displacement is small Period of a pendulum where L = length of pendulum Example: pendulumpendulum  for  small L Restoring force Equilibrium position Velocity PhET

REP: 2007-Nov-28SHM14 Summary: Simple Harmonic Motion Hooke’s Law where x = displacement k  spring constant Period of a pendulum where L = length of pendulum g = accel. due to gravity Period of spring oscillator where m = mass k = spring constant

REP: 2007-Nov-28SHM15 Definitions: Vibrations & Waves Simple (middle school) definitions are: Vibration – “a wiggle in time” Wave – “a wiggle in space and time”