Happy Thursday! Get ready for warm up #9 Warm ups are due tomorrow! Pick up the paper on the front table and grab a calculator Get ready to take notes: we are starting on a new unit!! REP: 2007-Nov-28SHM1

A box slides along the frictionless surface shown in the figure. It is released from rest at the position shown. Is the highest point the box reaches on the other side at level a, at level b, or level c? A.At level a B.At level b C.At level c

A box slides along the frictionless surface shown in the figure. It is released from rest at the position shown. Is the highest point the box reaches on the other side at level a, at level b, or level c? A.At level a B.At level b C.At level c

Simple Harmonic Motion “back & forth”

REP: 2007-Nov-28SHM5 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 Oscillations Restoring force  brings an object back to its equilibrium position If simple harmonic motion is occurring, there are oscillations

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

A mass hung from a string tied at one end to a pivot point is free to swing down by gravity and then out and up because of its inertia, or tendency to stay in motion The forces of gravity act on the pendulum to restore it to it’s equilibrium position What is a pendulum? REP: 2007-Nov-28SHM7

Pendulum examples REP: 2007-Nov-28SHM8

What is the period of a pendulum? The period of a pendulum is the time it takes the pendulum to make one full back-and-forth swing. REP: 2007-Nov-28SHM9

Factors that effect the period of a pendulum Length of the string Starting angle (height) of the pendulum Mass DOES NOT effect the period of a pendulum foucault pendulum conservation of energy REP: 2007-Nov-28SHM10

REP: 2007-Nov-28SHM11 T= period of time L= length of pendulum g = acceleration due to gravity Formula for the period of a pendulum

FORMULA FOR THE PERIOD OF A A SPRING REP: 2007-Nov-28SHM12 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-28SHM13

REP: 2007-Nov-28SHM14 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 SHM15 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-28SHM16

REP: 2007-Nov-28SHM17 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-28SHM18 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-28SHM19 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-28SHM20 Definitions: Vibrations & Waves Simple (middle school) definitions are: Vibration – “a wiggle in time” Wave – “a wiggle in space and time”