CHapter11
Section 2 solving simple
harmonics
Objectives
Identify
the amplitude of vibration.
Recognize
the relationship between
period and frequency.
Calculate
the period and frequency of an
object vibrating with simple harmonic
motion.
Amplitude
In
the absence of friction, a moving
trapeze always returns to the same
maximum displacement after each swing.
The
amplitude is the maximum
displacement from equilibrium.
Periods and frequencies
The period (T) is the time (in seconds) it takes
for one complete cycle of the motion.
The SI unit of period is seconds (s).
The frequency ( f ) is the number of complete
cycles that occur in one second.
The SI unit of frequency is s-1, which is called a
hertz (Hz).
Periods and frequencies
Period
and frequency are inversely
related:
1
1
f or T
T
f
Since frequency is cycles per second
and since period is seconds per cycle,
frequency and period are reciprocals
of each other:
Measuring of simple harmonics
Period of a simple pendulum
The
period of a simple pendulum
depends on the length and on the freefall acceleration.
L
T 2
ag
length
period 2
free-fall acceleration
• The period does not depend on the mass of the
bob or on the amplitude (for small angles).
Example 1
An
orangutan on a swing swings in simple
harmonic motion with a period of 4.2 s.
Calculate the length of the cables
supporting the swing.
Example 2
You
need to know the height of a tower
But darkness obscures the ceiling. You
note that a pendulum extending from the
ceiling almost touches the floor and that
its period is 12s. How tall is the tower.
Student guided practice
Do
problems 1-3 in your book page 375.
Period of mass system
The
period of an ideal mass-spring system
depends on the mass and on the spring
constant.
mass
m
period 2
T 2
spring constant
k
• The period does not depend on the amplitude.
• This equation applies only for systems in which the
spring obeys Hooke’s law.
Example
The
body of a 1275kg car is supported on
a frame by four springs. Two people riding
in the car have a combined mass of
153kg. When driven over a pothole in the
road the frame vibrates with a period of
0.840s. Find the spring constant of a single
spring.
Student guided practice
Do
problems 1-2 in your book page 377.
homework
Do
worksheet problems 1-5
closure
Today
we learned about period and
frequency
Next we are going to learn about waves
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