87.2 Simple harmonic oscillation x(t)=Acos(@t +o) +4 v(= dx(t)=-Aasin(at+P)E o d d'x(t (a) a()= +a4 dt -A@ cos(at +o) (b) +x.p=0a=-a x=0v=-V.a=0 x=-X.=0a=+a 87.2 Simple harmonic oscillation 4. How to determine if an oscillatory motion is simple harmonic oscillation? (criterion) Criterion 1: F total One force or the sum of several forces Criterion 2: k +“x=0 Criterion 3: x(t)=Acos(at+o)5 §7.2 Simple harmonic oscillation x(t) = Acos(ωt +φ ) sin( ) d d ( ) ( ) = = −Aω ωt +φ t x t v t cos( ) d d ( ) ( ) 2 2 2 = − ω ω +φ = A t t x t a t m m m m m x x v a a x v v a x x v a a = − = = + = = − = = + = = − 0 0 0 0 +A +A +ωA −ωA A 2 +ω A 2 +ω φ=0 4. How to determine if an oscillatory motion is simple harmonic oscillation?(criterion) F kxi ˆ total = − r Criterion 1: One force or the sum of several forces Criterion 2: 0 d d 2 2 + x = m k t x Criterion 3: x(t) = Acos(ωt +φ ) §7.2 Simple harmonic oscillation