大学物理课件-振动3

5)cos(111ϕω+=tAx)cos(222ϕω+=tAx21xxx+=)cos(11ϕω+=tA)cos(22ϕω++tA)cos(ϕω+=tAx)cos(212212221ϕϕ−++=AAAAA22112211coscossinsintanϕϕϕϕϕAAAA++=)cos(111ϕω+=tAxx1Avϕ12Avϕ2Avx2x1xx2NQM1M2ϕM)cos(222ϕω+=tAxPx=x1+x2OOM1M)(π121ϕϕ−−=∠MOM)](πcos[2122122212ϕϕ−−−+=AAAAA)cos(212212221ϕϕ−++=AAAAAONMN=ϕtan22112211coscossinsinϕϕϕϕAAAA++=)cos(212212221ϕϕ−++=AAAAA2121AAAAA+≤≤−™k=0,1,2…™ϕ2ϕ1=2kπcos(ϕ2ϕ1)=1=A1+A2=Amax2122212AAAAA++=Amax=2A1A1=A2k=0,1,2…™ϕ2ϕ1=(2k+1)πcos(ϕ2ϕ1)=–1=Amin2122212AAAAA−+=21AA−=A1=A2Amin=0)3π3cos(4.01+=tx)6π3cos(3.02−=tx(1))3cos(5.033ϕ+=txOx1Av2AvAvπ/3–π/6ϕ(2)ϕ3ϕ3(1)ϕ1ϕ2=π/24.03.0tan=α2221AAA+=α=∠OAA1=0.5(m)π21.0=απ12.03/π=−=αϕ)π12.03cos(5.0+=tx(2)ϕ3=ϕ=0.12πAmax=A1+A2=0.5+0.5=1.0(m)ϕ3=ϕ+π=1.12πAmin=A1A2=0.50.5=0(m)ntaxωcos1=CRRAδ1a2av3avϕM)cos(2δω+=tax)2cos(3δω+=tax…])1(cos[δω−+=ntaxnvC:R)cos(ϕω+=tAxOC1av2avRRAQϕδMCO=nδ2sin2δnRA⋅=2sin2δRa⋅=)2/sin()2/sin(δδnaA=)π(21δnCOM−=∠)π(21δ−=∠CONCOMCON∠−∠=ϕδ)1(21−=nDMPCQ=δOCN=δ∆MCOxN∆OCNP)cos(ϕω+=tAx)21cos()2/sin()2/sin(δωδδ−+=ntna)2/sin()2/sin(δδnaA=Fδ=2kπk=0,1,2…A=nankπ2′=δk’k’nFk′=1,2…,(n-1),(n+1),…nδ=2k′πA=01Av),cos(111ϕω+=tAx2Av)cos(222ϕω+=tAx)()(1122ϕωϕωϕ+−+=∆tt)()(1212ϕϕωω−+−=tx=x1+x2)cos(11ϕω+=tA)cos(22ϕω++tAϕ1=ϕ2=0ttAx)2cos()2cos(21212ωωωω+⋅−=ω2ω1,ω2ω1ν2ν1ω2ω1(,ω2ω1ν2ν1x=x1+x2tA1cosω=tA2cosω+ttAx)2cos()2cos(21212ωωωω+⋅−=ω2∼ω1ω2−ω1ω2+ω1ttAxωcos)(=tAtA)2cos(2)(12ωω−=)2cos(cos12ttωωω+=ttω2ω1(,ω2ω1ν2ν11Avν121(ν2−ν1)2Avν21Av2Av(ν2−ν1)(ν2−ν1)(ν2−ν1)(ν2−ν1)ν=(ν2−ν1):ν=|ν2-ν1|6xyOA1A1A2A2)cos(11ϕω+=tAx)cos(22ϕω+=tAy0.112=−ϕϕ21AyAx=xAAy12=22yxs+=)cos(2221ϕω++=tAAxAAy12−=π.212=−ϕϕxyOA1A1A2A2)cos(11ϕω+=tAx)cos(22ϕω+=tAy2π.312=−ϕϕ1222212=+AyAxyxxyOA1A1A2A22π.412−=−ϕϕxy1222212=+AyAx)cos(11ϕω+=tAx)cos(22ϕω+=tAy5.)(sin)cos(21221221222212ϕϕϕϕ−=−−+AAxyAyAx∆ϕ=5π/4∆ϕ=3π/2∆ϕ=7π/4∆ϕ=0∆ϕ=π∆ϕ=π/2∆ϕ=3π/4Q∆ϕ=π/4P·.∆ϕ=5π/4∆ϕ=3π/2∆ϕ=7π/4∆ϕ=0∆ϕ=π∆ϕ=π/2∆ϕ=3π/4Q∆ϕ=π/4P·.1.2.(P198)