Page 1

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Oscillatory Systems

θ

m. l

d

2

d t2

m . g . sin ( θ ) 0

x

I.

For small θ, 2 g. d θ θ 0 l 2 dt

T

ω

m

d

2

d t2

c

c .θ 0

θ ω

2 c

I

2 g

l

θ

x

I mg T

m

T x

m.

k m x

d

2

d t2

ω

2

k m

x

k.x 0

2l m.

d

2

d t2

x

x 0 l 2 2.T ω l .m

2 .T .

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a”‚[û


x

ρ

m

ρ .l .

2x

d

2

d t2

2.ρ .g .x 0

x

where l is the length of the fluid column 2 g ω 2. l

m.

d

2

d t2

x

A . ρ .g . x 0

where A is the cross-sectional area of the tube 2 A.ρ .g ω m

L

q C

L.

d

2

d t2

ω

2

q

q 0 C

1 L .C

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a”‚Z˜


phase.mcd

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1B24 Waves Optics and Acoustics Lecture 1 of 33 (UCL)  

1B24 Waves Optics and Acoustics Lecture 1 of 33 (UCL)