 m=1 кг w=10 рад/с C=500 Н/м 2L=20 см => L=0,1 м без трения
xmax-? Nz max-?
В векторной форме: mar = F+N+ФeФk
На ось ох: mx''=-Fупр+Фe Fупр=C(x-L) Фe=mw2x
На ось oy: my''=Ny-mg y''=0 => Ny=mg
На ось oz: mz''=Фk-Nz Фk=m2wx' z''=0 => Nz=2wx'm
mx''=mw2x-C(x-L)
x''+(C/m - w2)x=CL/m
x''+(C/m - w2)x=0 - однор. ур.
l2=-(C/m - w2)
l2=-400
l1,2=+-20i
xo.o.=C1cos20t+C2sin20t
xч.н.=CL/(C-w2m)
x=C1cos20t+C2sin20t+(CL)/(C-w2m)
x'=-20C1sin20t+20C2cos20t
Н.у: t=0 x(0)=L x'(0)=0
L=C11+C20+(CL)/(C-w2m) => C1=L(C-w)2m - (CL)/(C-w2m) = -(Lw2m)/(C-w2m)
0=-20C1*0+20C2*1 => C2=0
x=-(Lw2mcos20t)/(c-w2m)+(CL)/(C-w2m)=[L(C-w2mcos20t)]/(C-w2m)=x(t)
x'=(20Lw2msin20t)/(C-w2m)
x=xmax => x'=0 => sin20t=0 => 20t=П => t=П/20
xmax=x(П/20)=[L(C+w2m)]/(C-w2m) = 0.15 м
Nz=2wm*(20Lw2m)/(C-w2m)*sin20t
Nz mzx=(40Lw3m2)/(C-w2m)=10 H
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