Simple Harmonic Motion Reminders: Syll. State Due Tuesday WA due Tuesday Quiz Tuesday

Oscillations—what are they?  Repetitive, cyclical motion in which a mass (particle) moves back and forth around a single fixed point with a regular frequency  A.k.a Harmonic motion, or periodic motion  Examples:  The “sting” of a ball hitting a bat  Strings on a violin that is being bowed  The swaying of buildings in wind or in earthquakes  And many, many more…

So…what causes oscillations?  Restoring Force:  When a particle is displaced from its equilibrium position, it wants to return to that point  The force applied to a particle in order to bring it back to its equilibrium is called the restoring force  When the restoring force varies at a regular rate from + F max to – F max and back again, the object is oscillating due to this restoring force

Magnitude of Force…  Depends on the displacement from equilibrium  Always (ALWAYS) is in the direction pointing toward the equilibrium point  Hooke’s Law:

Simple Harmonic Motion

Wait…where’d that equation come from?

Oscillations—position vs time  What pattern do we see when we plot a graph of position vs. time for an oscillating mass?

Simple Harmonic Motion (SHM)

Let’s define those variables a bit more:  Displacement: The position, measured from the equilibrium point, of the particle at any time t in its oscillation  Amplitude: the maximum displacement of a particle from its equilibrium position

Angular Frequency vs. Frequency  Frequency: the rate at which oscillations occur. Measured by counting the number of times an oscillating particle passes by a fixed point each second.  units = s -1 (or, cycles per second)  Angular Frequency: the rate at which oscillations pass through the radian measure of an oscillation.  Typically—units are in radians per second (rad∙s -1 )  1 oscillation = 2 radians

Frequency and angular frequency… quantified  Frequency (f), measured in Hertz (Hz) or sec -1  Angular frequency (), measured in rad∙s -1

What will cause the frequency to change?  Frequency of an oscillating mass…  Does NOT depend on the amplitude  DOES depend on the spring constant  DOES depend on the mass

Frequency vs. Period

Phase Constant,   The phase constant is a value given to show at what point in the oscillation the timer had begun.  In other words, at what radian position was the oscillating mass at time t = 0 sec.?  Units = radians Similarly, Phase difference is the difference in radian position at time t=0 for 2 waves or oscillating masses