Download This net force causes the bob to slow down.

Harmonic Motion in Pendulums
NOOOOOO!
The period of
oscillation is
independent of
my fear!
WHS 2014/2015
Lee Wignall
So you pull it back…..then what?
Notice how the only time the tension and gravity are equal and opposite is
when the bob is straight down.
That means there is a NET FORCE in any other position.
There are two net forces:
1) Since there is less gravity acting against tension as it rises, there is a
net centripetal force (toward the center). This is what causes the bob
to turn.
2) There is also a new net force directed backward because of the angle
between tension and gravity. This net force causes the bob to slow
down.
Warm up questions
1. Why does a pendulum follow a curved
path?
2. Explain why a pendulum speeds up, slows
down, and momentarily stops at various
points in its path.
So you pull it back…..then what?
Notice how the only time the tension and gravity are equal and opposite is
when the bob is straight down.
That means there is a NET FORCE in any other position.
There are two net forces:
1) Since there is less gravity acting against tension as it rises, there is a
net centripetal force (toward the center). This is what causes the bob
to turn.
2) There is also a new net force directed backward because of the angle
between tension and gravity. This net force causes the bob to slow
down.
Equilibrium and Restoring Force
Equilibrium: The position in a system where the net force is zero. The natural
“resting” point of a system. The position the system strives to achieve.
Restoring force: a force that drives a system back toward equilibrium.
equilibrium
This component of gravity is
the restoring force.
Equilibrium and Restoring Force
As the pendulum swings back to the equilibrium point the net force
becomes zero again. However, it swings PAST that point due to inertia
(Newton’s 1st Law) and the process begins all over again in the
opposite direction.
Angular Velocity, Period, and Frequency of Oscillation of a Pendulum
For circular motion:
R
L
For pendulum motion:
Sooo, the frequency of a pendulum’s swing is:
f = ___
2π
and since T = 1/f 
a
Sample Problems
What is the period of a pendulum that is 1.5 meters
long? What is its frequency?
How many times will it oscillate (make a full cycle) in
10 seconds?
Sample Problems (answers)
What is the period of a pendulum that is 1.5 meters
long? What is its frequency?
T = 2.46 s
f = 0.41 Hz
How many times will it oscillate (make a full cycle) in
10 seconds?
It will oscillate 4.1 times
Where will the pendulum be in 10 seconds?
(predict with 2 different masses)