Simple Harmonic Motion Guided Notes
Name:______________ Class:_________
Do Now
Explain why a pendulum oscillates using words and pictures.
Vocab Review!
What does the word oscillation mean?
When is oscillatory motion is called periodic motion?
We refer to these repeating units of periodic motion as __________________.
The time it takes to complete one cycle is called the _____________________.
Example: Earth’s rotation has a period of 24 hours, or 86,400 s
Simple Harmonic Motion
Pendulums and springs are special examples of motion that not only oscillatory and periodic, but also ______________.
Simple harmonic motion is a type of periodic motion in which the ____________________________________________
__________________________________________________________________________________________________
e.g. greater displacement = greater force
Restoring Force – CFUs
In which position(s) is the restoring force of the pendulum …
… greatest?
… zero?
… angled downward and towards the right?
A
B
C
D
In which position(s) is the restoring force of the sp
… greatest?
… zero?
… directed upwards
Springs can also be compressed!
Any _______________ (stretchable) material will act somewhat like a spring.
Calculating Net (Restoring) Force
In pendulums …
In springs …
Look at the diagram.
Fspring = kx
What forces cancel out?
Where k = spring constant
x = displacement
What is the net force?
E
F
G
We Do: Calculating Net (Restoring) Force
An engineer measured the force required to compress a spring.
Force (N)
Displacement
(mm)
2
1.0
3
1.5
4
2.0
5
2.5
6
3.0
1) Based on the data, what is the spring constant?
2) Predict the force required to compress the spring by 3.5 mm.
Note: Amplitude ______________ affect
period in pendulums or springs!
Turn and Talk
1) If you stretch and release a slinky, you will notice that the amplitude of its motion decreases over time (why?).
How does this decrease in amplitude affect the period of motion?
2) Will a grandfather clock run slower or faster if placed on the moon? Why?
3) How does doubling the mass affect the period of a pendulum? How does doubling the mass affect the period of
a spring
Conservation of Energy
Ideally, pendulums and springs both conserve energy. (Realistically, they
lose energy over time due to __________________________).
In both cases, PE is maximum at _____________________________.
PE gradually converts to KE, and reaches zero at the equilibrium point.
KE shows the opposite trend – it is maximum at equilibrium and
reaches zero at maximum displacement.
We have a simple formula for the PE in a spring.
PEspring =
You Do Problems
1) A spring stretches by 18 cm when a bag of potatoes weighing 56 N is suspended from its end.
a) Determine the spring constant, k
b) How much EPE does the spring have when it is stretched this far?
2) A pendulum swings from its release point, past equilibrium, to its highest point on the opposite side in 0.4 seconds.
The highest point is 8 degrees above equilibrium. What is its frequency? Its period? Its amplitude?
3) 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 12 s. How tall is the tower?
4) Billie releases the bob of his pendulum at an angle of 10° from the vertical. At the same time, Bobby releases the bob
of his pendulum at an angle of 20° from the vertical. The two pendulums have the same length. Does Billie’s bob reach
the vertical position before, after, or at the same time as Bobby’s bob? Explain.
Damping and Resonance
Damping is the ______________________________ of a wave.
All real pendulums and springs have damping.
•
________________________________________________________________
•
Amplitude of motion becomes smaller, until it ceases
Some systems are designed to heavily damped, such as

shock absorbers on a car

Damping mechanisms in the foundations of buildings in earthquake zones
Resonance is ____________________________________________ of oscillation of a system that occurs when an
______________________________________________________________________________________________ –
the frequency it would naturally oscillate at if hit once.
Examples:
Pushing a child on a swing
Shattering a kidney stone with ultrasound
Vibration of the strings that differ by one or more octaves (and to a lesser extent, other harmonic intervals) when a note
is played on a stringed instrument.
Shattering glass with your voice
Tacoma-Narrows Bridge