1. 7-1 Simple Harmonic Oscillation

2. Remember!!!
삼각함수는
공학에서
가장 중요한 함수!

3. Simple Harmonic Oscillation (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:

4. Simple Harmonic Oscillation (2)
Let’s define the angular frequency:
Then we have
What is the solution of this equation?

5. Differentiation of Trigonometric Functions

6. Exercise Show that x(t) = A cos(ω t + φ )
Satisfies the following equation:
A, ω, and φ are constants.

7. Notice!!!
신호(Signal)는
삼각함수이다!

8. 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)

9. Sinusoidal Motion
T = 2π /ω A t
y(t)=Asin(ωt+φ)

10. Variables Amplitude A Angular Frequency ω Frequency ν = (ω / 2π)
ν = (ω / 2π)
Period
T = 1/ν = (2π/ω)
Initial Phase φ