Pendulum Simple Harmonic Motion

Pendulum  A simple pendulum is one which can be considered to be a point mass suspended from a string or rod of negligible mass. It is a resonant system with a single resonant frequency.

Characteristics of a Pendulum  L = Length  M = Mass  T = Period  F = Frequency  g = Gravity  Pe = Potential Energy  Ke = Kinetic Energy

Characteristics of a Pendulum  Length is the distance from the fulcrum to the center of mass of the pendulum.  For our pendulum, we cheated…  How?

Characteristics of a Pendulum  We assumed that our string was weightless and we were a little “Cavalier” in our measurements of where the center of mass occurred.  Yesterday I asked about “Big Ben”…  Will adding “pennies” to the pendulum change the period of the swing? Why?

Characteristics of a Pendulum  Period is the time it takes to make one cycle  Frequency is the number cycles that occur in one second  They are inverse to each other

Characteristics of a Pendulum  T = 1 / F  F = 1 / T

Characteristics of a Pendulum  Which characteristic is most important in determining the motion of a pendulum?  Length

Characteristics of a Pendulum  We saw, in our experiments, that changing the mass of the “bob” had essentially no effect on the swing of our pendulums.  Any differences that we saw is easily explained on your experimental “Human Error”.  (Yes… You messed up…)

Characteristics of a Pendulum  Period of a pendulum is based on length and gravity.

Characteristics of a Pendulum  Would the motion of a pendulum vary on the Moon? Why? How?

Characteristics of a Pendulum  We can also look at a graph of the motion of a pendulum and see that it shows a sine wave for both a d vs. t graph and a v vs. t graph.

Motion of a Pendulum

 These graphs are based on the premise that there is no friction.

Energy of a Pendulum  PE = mgh  KE = ½mv 2

Energy of a Pendulum  Discuss this motion. Be able to explain what is happening as the pendulum moves through a series of cycles.