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## Pendulum

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**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 = m•g•h • KE = ½•m•v2**Energy of a Pendulum**• Discuss this motion. Be able to explain what is happening as the pendulum moves through a series of cycles.