Mi Tarea

Problema 3-10
Mx+Cx+Kx=(meω2)senωt
meω2senωt=Feiωt
x=xei(ωt-φ)=xe-iφeiωt=Xeiωt
(-ω2M+iCω+K)Xeiωt=Feiωt)
X=FK-ω2M+i(Cω)
Problema 3-11
ω=120060=20RPS=20*2πrads
ωn=18cps=18*2πrads
ωωn=1.111xt=x1e-ξωntsen1-ξ2ωnt-ϕ1+meω2senωt-ϕk-mω22+cω2
t=0
x0=0
0=-x1senϕ+meω2ksen-ϕ1-ωωn22+2ξωωn2…………1
t=0
x(0)=0
xt=x1e-ξωnt1-ξ2ωncos1-ξ2ωnt-ϕ1-ξωnsen1-ξ2ωnt-ϕ1+meω2ksen-ϕ1-ωωn22+2ξωωn2………2x0=0=x11-ξ2ωncosϕ1+ξωnsenϕ1+meω2kωcosϕ1-ωωn22+2ξωωn2
x1senϕ1=-meω2kωsenϕ1-ωωn22+2ξωωn2

x11-ξ2ωncosϕ1+ξωn-meω2kωsenϕ1-ωωn22+2ξωωn2+meω2kωcosϕ1-ωωn22+2ξωωn2=0
dividiendo
tanϕ1=-1-ξ2senϕξsenϕ-ωωncosϕ………3Problema 11
en t=∞, trasciend term=0 y e-ξωnt→0
amplitud final=x∞=meω2ksenωt-ϕ1-ωωn22+2ξωωn2

tanϕ=2ξωωn1-(ωωn)2=.21.1111-1.1112=-.44755
ϕ=-43.457°
en ϕ1para 3 tanϕ1=-.7820, ϕ1=142°
Problema3-12
f=12πkm, donde k=48EIl3, I=πd364, m=mdisco+0.486m
k=4829x106π(12)4243*64=309libin
.486m=.486.283π412224386=.648386
m=10386+.648386=10.65386
f=12π309*38610.65=16.84cps=1028 RPM
Problema 3-13w=10 lib=44.48N, m=44.489.81=4.534kg, g=386mseg2=9.81mseg2
k=48EIl3=E=200x109Nm2l=2*.3048=.6096md=.5*2.54x10-2=1.270x10-2mI=πd364=.1277x10-8
k=54116Nm
.486m=.485xπ41.270x10-2.6096xρ=.2938ρ=7830kgm3=densidad del metal
f=12π541164.534+.2938=16.86Hz
Problema 3-14
dia=2.54cm, I=πd364=π*41.6264*1004=2.043x10-8m4
k=48EIl3=48*200x109*2.043x10-8.40642=2.922x106Nmm=13.6+.486π4*2.542*.40647830=13.6+784=14.38kg
fm=12π2.922x10614.38=71.74Hz=4304RPM
ωωn=60004304=1.394
γ=eωωn21-ωωn2=-2.060e
me=.2879kgcm tenemos, e=.287913.6=.02117cm
γ=-.2060.02117=-.04316cmF=mγ+eω2=14.38-.04316+.02117100(2π*100)2=1273N
diametro=1.405cm
.486m=.486π4*.019052*.40647830=.4408
m=mdisc+.483m=14.04kg
I=π64*1.4054*1004=.6464x10-8
k=48200x109*.6464x10-8.40643=.9441x106
fm=41.27Hz=2476RPM, ωωn=60002476=2.423γ=.02117(2.423)21-(2.423)2=-.02552, γ+e=.00435
F=14.042.00435100(2π*600060)2=241.1N
Problema 3-15
η=η0+eωt2
.0508=0+.02122π*100t2
t=.05086.6602=.0075seg
Problema 3-16
mx=-kx-y, donde x...