a = - A ω² sin(ωt) = - (2πf)² A sin(2πf t) = - ω² y
v = Aω cos(ωt) = 2πf A cos(2πf t)
y = A sin(ωt) = A sin(2πf t)
Simple
Harmonic
Oscillations
ω = 2πf
Relation to
Uniform Circular Motion
Maximum displacementAmplitude
1 Hertz = 1 Hz = 1 cpsCycles per time
f = 1/T
f = Frequency
Time per cycleT = Period
Periodic Motion
FG = G m1 m2 / r²
Every object in the universe is attracted to every other object
with a force that is directly proportional to their masses and
inversely proportional to the square of the distance between them.
Newton's
Law of
Universal
Gravitation
α = d ω / dt = d² ω / dt²
α = Δ ω / Δ t
Angular
Acceleration
ω = d θ / dt
ω = Δ θ / Δ t
Angular
Velocity
θ
Angle
Angular
quantities of
motion
ac = r ω²
Radial
Acceleration
at = r α
Tangential
Acceleration
v = r ω
s = r θ
Connection between
linear and angular
quantities:
Radian, Degree, Revolution:
1 rev = 360⁰=2π
ω² = ω₀² + 2 α θ
θ = ω₀t + ½ α t²
ω = ω₀ + αt
θ = ωt
Equations of motion
for: Angle,
Angular Speed, and
Angular Acceleration
Directed toward
center of curve
ac = r ω²
ac = v² / r
Centripetal
Acceleration
Uniform
Circular
Motion
Unit VII
Phys
1401/2425