Fomula Sheet for Physics 221 Final (don’t forget to look at the other two
sheets though!)
Notes:
A bolded variable such as
p
indicates that the variable should be treated as a vector
A * in front of an equation indicates that the equation will be given to you
on the Final (The same equations as those on Practice Test 3)
Only the equations marked as such on this sheet will be given to you for the
Final. Equations marked on the previous two sheets will not be given.
The Simple Pendulum
T
= 2
π
s
L
g
f
=
1
T
Forced oscillations
A
=
F
0
m
q
(
ω
ext
2

ω
0
2
)
2
+
bω
m
2
You don’t need to memorize this equation.
I am listing it because it shows a
good point. The important thing to remember from the equation is that the
Amplitude of a Forced Oscillation is small, unless the frequency of the driving force
(
ω
ext
) is close to the natural frequency (
ω
0
). When this occurs the Amplitude
becomes very large and we have resonance. Understanding ideas like this is what we
mean when we ask you to understand the concepts of physics, and not just worrying
about whether you have the equation memorized or not. There will be a lot of
conceptual questions on the test, and you will need to make an effort in your
studying to understand the concepts we’ve gone over if you want to do well.
Traveling Waves
y
(
x, t
) =
Asin
(
kx

ωt
+
φ
)
describes a wave traveling in the +x direction
y
(
x, t
) =
Asin
(
kx
+
ωt
+
φ
)
describes a wave traveling in the x direction
In these equations,
k is wavenumber with
k
=
2
π
λ
1
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ω
is the angular frequency with
ω
=
2
π
T
= 2
πf
φ
is the phase constant
λ
= wavelength,
f
= frequency,
T
= period
v
=
λf
=
λ
T
=
ω
k
v is the speed of the traveling wave
Also, for waves on a string
v
=
s
F
μ
where
F
is the force being used to generate the wave, and
μ
is the thickness of the
string
The energy
E
of the wave is proportional
A
2
The power
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 Spring '08
 HAND
 Physics, Thermodynamics, Energy, sound wave

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