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.