, . , . . .
|
|
X1 X2
, , . . . .
ωI SI1(t)=S20sin(ωI*t+φI)
SI2(t)=S10sin(ωI*t+φI)
ωI, SI20/SI10=1
ωI=√(k/m)
ωII SII1(t)=SII20*sin(ωII*t+φII)
SII2(t)=SII10*sin(ωII*t+φII)
ωII, SII20 / SII10 = -1
ωII=√((k+2k1)/m)
S1(t)=SI10*sin(ωI*t+φI)+SII10*sin(ωII*t+φII)
S2(t)=SI20*sin(ωI*t+φI)+SII20*sin(ωII*t+φII)
ωI,ωII, SI20/SI10, SII20 / SII10 }à
S1(0), S1'(0) S2(0), S2'(0) } → SI10; φI SII10; φII
, ω1, . , , ω2.
ωI ≈ ωII, |ωI ωII | <<ωI ≈ ωII, . , . . ωI ≈ ωII, |ωI ωII |. T=2p/(ωI ωII). Δω=ωI ωII <ω>=(ωI +ωII)/2 S1(t)=2*S1(t)*(cos( Δω/2)t) *cos(<ω>t) S2(t)=2*S1(t)*(sin( Δω/2)t) *cos(<ω>t).
. , . , , .
|
|
U=kx2 /2=kx2cos2(wt+p)/2=kX2(1+cos2(wt+p))/4;
Tk=mV2/4(1- cos2(wt+p))/4; , . V=wX; W=Tk+U=kX2/2=mV2/2;
, , .
. Q . 2p , . Q .Q=p/Q, Q .
21.
2.
2 . , . . , . : , , , . Y(x,t)=f1(t-x/v): Ox. Y(x,t)=f1(t+x/v): Ox. . . , . , . . . . : S*(t)=S0sin(wt+j*) . . . .: S(t)=S0sin[w(t(x/c))]
S=S(0)*cos(wt-2p*x/l)=s(0)*os(wt-k*x) , l=
. . . =w(t(x/c)) const., w(Dt(Dx/c))=0, (Dx/Dt)=c .S(t,x)=S0sin[w(t(x/c))] S(t,x)=S0sin[wtkx], k . : k=w/c=2p/(Tc)=2p/l; : = k , n . ={kx; ky; kz;} Þ S(x, y, z, t)=S0sin(wtkxxkyykzz).
: S(t,r)= cos(wtkr), r .
: S(t,r)= cos(wtkr), r .
22
.
S(t,r)=S0sin(wt ); 2S/t2=w2S; Þ
2S/x2+2S/y2+2S/z2=S(kx2+ ky2+kz2)=Sk2
2S/(t2c2)=2S/x2+2S/y2+2S/z2
2S/t2=DS/c2, DS . c=w/k
.
S=S(t /c)
23.