Lesson 5
PENDULUMS
AP Physics B Standards

I.F.3. Pendulums
b) Apply the expression for the period of a simple pendulum.
c) State what approximation must be made in deriving the period.

I.F.1. Simple Harmonic Motion
LESSON 5:
Pendulums
g) State how the total energy of an oscillating system depends on the
amplitude of the motion, sketch or identify a graph of kinetic or
potential energy as a function of time, and identify points in the
motion where this energy is all potential or all kinetic.
h) Calculate the kinetic and potential energies of an oscillating system
as functions of time, sketch or identify graphs of these functions, and
prove that the sum of kinetic and potential energy is constant
Lesson Objectives
Students will be able to:
1.
describe how several variables impact the period of a pendulum.
2.
represent kinetic and potential energy graphically at various
points in the pendulum’s motion.
Pendulums


The pendulum can be thought of as a simple
harmonic oscillator.
The displacement needs to be small for it to
work properly.
Period of a pendulum
l
T  2
g
T: period (s)
 l: length of string (m)
 g: gravitational acceleration (m/s2)

Sample Problem 5.1:
Predict the period of a pendulum consisting of a 500 gram mass
attached to a 2.5-m long string.
Sample Problem 5.2:
Suppose you notice that a 5-kg weight tied to a string swings back and
forth 5 times in 20 seconds. How long is the string?
Sample Problem 5.3:
The period of a pendulum is observed to be T. Suppose you want to
make the period 2T. What do you do to the pendulum?
miniLab: Pendulums
Vary the length of the pendulum.
Time ten periods. Record in data table.
Linearize pendulum equation.
Plot on graph paper and determine “g” from
the slope.
Pendulum
Number of
oscillations
Elapsed
time (s)
Period
(s)
Length
(m)