Today’s Topic:
Simple Harmonic Motion Explanation
Learning Goal:
SWBAT name the parts of a wave, and
explain the relationship between frequency
and period.
 Describe the similarities that exist between
these two objects.
 Both are undergoing Simple Harmonic
Motion!
Homework
 Complete the Pendulum Lab
(Due Thursday, May 28 th).
 Complete the Simple Harmonic Motion
Worksheet. (Due Thursday, May 28th)
Vibration
 All things around us are constantly
wiggling and jiggling in place.
 However, most of these objects are
too small to see.
 What are some objects that
are currently wiggling and
jiggling in this room?
Vibration
 Objects in their natural state of rest are in
their equilibrium position.
 When objects move back and forth from
their equilibrium position, they are said to
be vibrating.
Vibration
 Vibrations need time in order to move
back and forth, or oscillate.
 The pendulum we see up here, as well as
the spring-mass system are examples of
objects that move in simple harmonic
motion.
 The true definition of simple harmonic
motion is a bit unwieldy, but here it is:
Vibration
 Simple harmonic motion is a type of
periodic motion where the force acting
on the object is directly proportional to
the displacement and acts in the direction
opposite of displacement.
 Let’s pick this apart with the spring-mass.
 For all intents and purposes, think of the
pendulum and spring-mass system here.
Period
 The time it takes for an oscillating object
to complete one full cycle is its period.
 In Physics, period is written as T, and is
measured in seconds.
 Think of T as the TIME it takes to
complete one full oscillation.
Period of a Pendulum
 What did our lab from yesterday tell us
about the period of a pendulum?
 Period of a pendulum only depends on:
 The length of the pendulum
 The acceleration due to gravity
Tpendulum = 2π
Length of Pendulum
Acceleration Due to Gravity
Tpendulum = 2π
𝐿
𝑎𝑔
Example Problem
 What is the period of a pendulum on
Earth with a length of 70 cm?
Answer: 1.679 s
 If this same pendulum were brought to Io,
one of the moons of Jupiter where the
acceleration due to gravity is 1.796 m/s 2,
how much longer would the period be?
Answer: 2.244 s
Period of a Pendulum
 Galileo Galilei was
the first to observe
and discover this
fact – the mass of
a pendulum has no
effect on its period.
Period of a Pendulum
 MIT’s Walter Lewin demonstrated this
discovery as well in one of his classes.
 Here, he compares the time it takes for
10 pendulum oscillations with and without
extra mass.
More S.H.M.
 The mass and spring also exhibit simple
harmonic motion.
 The period of the mass and spring
system depends only on:
 The mass at the end of the
spring
 The spring constant of the
spring
More S.H.M.
 This formula may be written as:
Tmass-spring = 2π
Mass
Spring Constant
Tmass-spring = 2π
𝑚
𝑘
Example Problem
 A mass-spring system oscillates with a
period of 0.45 seconds. What is the
spring constant of the spring if the mass
is 625 grams?
Answer: 121.847 N/m
Period and Its Inverse
 A 6.2 cm long pendulum oscillates very
quickly. What is the period of this
pendulum?
Answer: 0.5 s
 So how many seconds does it take per
swing?
 What if we wanted to know how many
swings it can make per second?
Period and Its Inverse
 Flip that upside-down!
 The period tells us how many seconds it
takes for one complete cycle to occur.
 If we wanted to know how many cycles
occur in one second, we would be asking
for its frequency.
Frequency
 The formula for frequency is:
f=
1
𝑇
frequency =
[Hz]
1
f T
1
Period
[s]
Frequency
 The units for frequency are the Hertz.
 They are named after the
German scientist
Heinrich Hertz – who did
extensive work in the field of
electromagnetism, as well as radio
transmission.
 He was the first to conclusively prove the
existence of electromagnetic waves.
Frequency
 Technically, a Hertz is a
s -1,
or
1
Second
 So the pendulum we found has “a
frequency of 2 Hz.”
 Fun Fact:
 FM Radio stations broadcast their signals in
the MHz range. What does M mean?
 When I listen to NPR on 93.9 FM, what is
the frequency that my radio is picking up?