Oscillations Flashcards
ω =
√k/m
a is max at
extreme pos
a is min at
mean pos
F =
-mω^2 x
PE =
1/2mω^2 x^2
KE =
1/2k(A^2 - x^2)
TE
1/2mω^2 A^2
At eq. pos x(o) =
mg/k
If obj is acc, T =
2pi√l/g+a
If obj is decell T =
2pi√l/g-a
If obj is acc in same direction, T =
2pi√l/√(g^2+a^2)
Damping oscillations
x(t) = A(o)/e^γt sin(ωt + θ)
ω for damping oscillations
√[k/m - b^2/4m^2]
Forced oscillator
x(t) = Asin(w(α)t + θ)
A = F(o)/m√[ω(o) - ω(α)^2] + (bω(α)/m)^2
Speed of transverse on string V =
√T/μ μ = mass/len
speed of sound waves in air v =
√b/ρ
Newton’s formula V =
√P/ρ
Laplace correction V =
√γP/ρ γ = Cp/Cv
Speed increases when humidity
increases
Energy density u =
1/2 ω^2A^2
Intensity I =
uV
Beat freq f(B) =
|f1-f2|
Fundamental node, L =
λ/2
Fundamental node f(o) =
V/2L
Open organ pipe, f(n) =
nf(o)
f(o) = V/2L
In open organ pipe _______ harmonics are present
All odd & even
Closed organ pipe, f(n) =
(2n-1)f(o) f(o) = V/4L
In closed organ pipes, ____ harmonics are present
odd
Resonance tube fn =
nV/4(Ln + e)
