87.2 Simple harmonic oscillation Angular frequency, period and frequency dx k k a2x(t)+x()=0 dt x(r)=Acos(ar+小)∴.a2 =—or Angular frequency a is related to the spring constant and the mass. It is decided by the nature of the system. Unit is rad/s The period T: x(t)=Acos(at+o) x(t+T)=Acos[o(t+r)+oI 87.2 Simple harmonic oscillation 2丌 OT=2丌T Unit is s Frequency v: v=2= 0=2元V 2兀 Unit is 1/s or Hertz(Hz). ② Amplitude dx(t) x(t)=Acos(at+o) v(t)=dr -Asin(at+o) Fo=x(0=Acos t=0 vo=v(0)=-A@sin o A=xm=x5+ The range of the oscillation is 2A=2x3 §7.2 Simple harmonic oscillation ① Angular frequency , period and frequency 0 d d 2 2 + x = m k t x x(t) = Acos(ωt +φ ) m k m k x t m k x t ∴ = = − + = ω ω ω or ( ) ( ) 0 2 2 Q Angular frequency ω is related to the spring constant and the mass. It is decided by the nature of the system. Unit is rad/s. The period T : ( ) cos[ ( ) ] ( ) cos( ) ω φ ω φ = + = + + = + x t T A t T x t A t §7.2 Simple harmonic oscillation ω π ω π 2 T = 2 T = Unit is s. Frequency ν : ω πν π ω ν 2 2 1 = = = T Unit is 1/s or Hertz (Hz). ②Amplitude x(t) = Acos(ωt +φ ) sin( ) d d ( ) ( ) = = −Aω ωt +φ t x t v t t =0 ω φ φ (0) sin (0) cos 0 0 v v A x x A = = − = = 2 2 2 0 0 ω v A x x = m = + The range of the oscillation is 2A=2xm