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Physics 1C
Lecture 12C
"Fluctuat nec mergitur. = She is swayed by
the waves but does not sink."
Motto of the city of Paris
Announcement
Problem solving sessions:
Heemin Kang (TA)
Wednesday 8 pm – 9:50 pm, Solis
107
Equations will be given for the quiz – no cheat
sheets
Simple Pendulum
The simple pendulum is another example of
simple harmonic motion.
Making a quick force diagram of the situation, we
find:
The tension in the string
cancels out with a
component of the
gravitational force (
mg
cos
θ
).
This leaves only the
perpendicular component
causing acceleration.
Simple Pendulum
q
=
max
cos (
w
t
+
f
)
In the tangential direction:
The length, L, of the pendulum is constant and
for small values of
:
This confirms the form of the motion is SHM !!!
The general solution is:
Simple Pendulum
The angular frequency is
The period is
The period and frequency depend only on the
length of the string and the acceleration due to
gravity
The period is independent of the mass
Pendulum Period
All simple pendula that are of equal length
and are at the same location (same
g
) oscillate
with the same period
Please note that the period of a pendulum
depends on different parameters than the
period of a massspring system
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Pendulum
Example
A 300g mass on a 30cm long string oscillates
as a pendulum.
It has a speed of 0.25m/s as
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 Spring '11
 Wethien

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