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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

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Pendulum

Pendulum

Simple Harmonic Motion


Pendulum1
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
Characteristics of a Pendulum

  • L = Length

  • M = Mass

  • T = Period

  • F = Frequency

  • g = Gravity

  • Pe = Potential Energy

  • Ke = Kinetic Energy


Characteristics of a pendulum1
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 pendulum2
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 pendulum3
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 pendulum4
Characteristics of a Pendulum

  • T = 1 / F

  • F = 1 / T


Characteristics of a pendulum5
Characteristics of a Pendulum

  • Which characteristic is most important in determining the motion of a pendulum?

  • Length


Characteristics of a pendulum6
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 pendulum7
Characteristics of a Pendulum

  • Period of a pendulum is based on length and gravity.


Characteristics of a pendulum8
Characteristics of a Pendulum

  • Would the motion of a pendulum vary on the Moon? Why? How?


Characteristics of a pendulum9
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 pendulum1
Motion of a Pendulum

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


Energy of a pendulum
Energy of a Pendulum

  • PE = m•g•h

  • KE = ½•m•v2


Energy of a pendulum1
Energy of a Pendulum

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


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