7-1 simple harmonic oscillation. remember!!! 삼각함수는 공학에서 가장 중요한 함수 !
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7-1 Simple Harmonic Os-cillation
Remember!!!
삼각함수는
공학에서
가장 중요한 함수 !
Simple Harmonic Oscilla-tion (1)
Hooke’s Law for the Restoring Force:
F = - k x Newton’s Second Law of Motion:
F = ma = m(dv/dt) = m(d2x/dt2)
Coupling of the Above Equations:
kxdt
xdm
2
2
Simple Harmonic Oscilla-tion (2)
Let’s define the angular frequency:
Then we have
What is the solution of this equation?
022
2
xdt
xd
m
k
Differentiation ofTrigonometric Func-
tions
)sin()cos( baxabaxdx
d
)cos()sin( baxabaxdx
d
Exercise
Show that
x(t) = A cos(ω t + φ )
Satisfies the following equation:
A, ω, and φ are constants.
022
2
xdt
xd
Notice!!!
신호 (Signal) 는
삼각함수이다 !
Determination of the Constants
x(t) = A cos(ωt+φ)
v(t) = (dx/dt) = −Aω sin(ωt+φ)
x(0) = A cos(φ )
v(0) = −Aω sin(φ)
Sinusoidal Motion
t
AT = 2π /ω
y(t)=Asin(ωt+φ)
Variables
Amplitude A
Angular Frequency ω
Frequency ν = (ω / 2π)
Period T = 1/ν = (2π/ω)
Initial Phase φ
A Quiz
• Sampling Frequency = 16,000 / sec• Data 사이의 시간 간격은 ?• 1,024 Data 사이의 시간 간격은 ?
Simple Harmonic Oscillation
)cos()cos()( tRRtx
)(tx
R 스프링에 매달린 추 물질 내부의 분자들 소리를 내는 공기분자들 안테나 속의 전자들
모두 삼각함수에 의해 기술된다 !
Transduction of Sound & Image through Microphone &
CCD
Modulation (Coding)
Oscillation Circuit
Transmission into Space
Receiving by Resonating Circuit
Demodulation (Decoding)
Transduction of Electrical Signal into Sound and Image
Telecommunication (1898-)
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