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