Simple Harmonic Motion
Physics 12
Joke of the day:
 Is it June yet?
Simple Harmonic Motion:
 Any motion that repeats itself precisely over equal periods of
time is called periodic motion
 If that periodic motion is generated by a linear restoring
force then it is simple harmonic motion (SHM).
SHM Examples:
Review:
 Period (T) is the time for one complete
oscillation.
 Unit = seconds
 Frequency (f) is the number of complete
oscillations per second.
 Units = Hertz (s-1 or 1/seconds)
1
f 
T
Restoring force:
 will tend to bring the system back toward equilibrium.
 is a function only of position of the mass or particle.
 is always directed back toward the equilibrium position of
the system.
A TRAMPOLINE exerts a restoring
force on the jumper that is directly
proportional to the average force
required to displace the mat.
Photo by Mark
Tippens
More SHM:
 Displacement: distance from equilibrium.
 Amplitude: maximum displacement
Review: Hooke’s Law:
F = -kx

F =restoring force of spring (N)
 (-) because the force acts in opposite direction of the displacement and
the applied force

K = spring constant (N/m)
 Each spring has it’s own constant

x = distance that the spring has been extended or compressed (m)
The amplitude, A, of a wave is the
same as the displacement ,x, of a
spring. Both are in meters.
CREST
Equilibrium Line
Trough
Springs are like Waves!
Review: Elastic Potential Energy:
 Symbol: Ee
Ee = ½
 k = spring constant (N/m)
 X= length of extension or compression (m)
 Units = N·m or J
2
kx
Conservation of Energy in Springs:
Total energy of mass and spring system:
 At any position (x) the total energy is:
 At either end, the mass stops, so velocity =0, also all elastic
potential energy
 At equilibrium, x=0 so all kinetic energy
Period of mass on spring:
Example 1:

If you stretch a spring a distance of 12.0cm from its rest
length and release it. A 125g mass on the end of the spring
completes exactly 20 cycles in 15.5 seconds. Find
a)
b)
c)
d)
e)
The period
The force constant of the spring
The total energy of the system
The maximum speed of the mass
The speed of the mass when it is 10.0cm from the
equilibrium
Period of a pendulum:
Example 2:
 Find the period of a pendulum with a 2.45kg bob and having
a length of 1.36m. By what would you have to increase the
length in order to double the period?
Try it :
 What is the frequency of a pendulum of length 0.75m that is
setup on the surface of Mars where the acceleration due to
gravity is about 1/3 of that on Earth?
 Page 608
 Questions 1-4
 Page 614
 Questions 5-8
(Answer:0.33hz)