{VERSION 6 0 "IBM INTEL LINUX" "6.0" }
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{CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 }{PSTYLE "Normal" 
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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 8 "restart;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 41 "eq := diff(x(t),t,t) + omega0^2*x(t) = 0;" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "sol := dsolve(\{eq, x(0)=x0
, D(x)(0)=v0\}, x(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "a
ssign(sol);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "x(t);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "E := 1/2*m*diff(x(t),t)^2 + \+
1/2*k*x(t)^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "E := simpl
ify(eval(E, omega0=sqrt(k/m)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 27 "Ek := 1/2*m*diff(x(t),t)^2;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "Ep := 1/2*k*x(t)^2;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "T0 := 2*Pi/omega0;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "Ek_s := int(Ek, t=0..T0) / T0;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 39 "simplify(eval(Ek_s, omega0=sqrt(k/m)));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Ep_s := int(Ep, t=0..T0) / T
0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "simplify(eval(Ep_s, o
mega0=sqrt(k/m)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "eq1 := A*cos(omega0*t + thet
a) = x(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "eq2 := eval(e
q1, t=0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "eq3 := eval(eq
1, t=Pi/(2*omega0));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "sol
ve(\{eq2,eq3\}, \{A,theta\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 18 "A := solve(eq2,A);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 
"theta := solve(eq3,theta);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
2 "A;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "x0 := 'x0'; v0 := \+
'v0';" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "X := unapply(x(t),
x0,v0,omega0,t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "V := un
apply(diff(x(t),t),x0,v0,omega0,t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 126 "plot(\{[X(1,0,1,t),V(1,0,1,t),t=0..2*Pi], \n      [X
(2,0,1,t),V(2,0,1,t),t=0..2*Pi],\n      [X(3,0,1,t),V(3,0,1,t),t=0..2*
Pi]\}); " }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 25 "\nTlumeny harmon
icky pohyb" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 
"restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "eq := diff(x(t
),t,t)+2*beta*diff(x(t),t)+omega0^2*x(t)=0;" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 44 "sol := dsolve(\{eq,x(0)=x0,D(x)(0)=v0\},x(t));" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "simplify(eval(eq, sol));" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "assign(sol);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "x(t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 43 "X := unapply(x(t), x0, v0, omega0, beta,t);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "plot(\{X(1,0,1,1/8,t), \n   \+
   limit(X(1,0,1,beta,t), beta=1), \n      X(1,0,1,4,t)\}, t=0..6*Pi);
" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "Kriticke tlumeni (beta = om
ega0)" "6#*&%)KritickeG\"\"\"-%(tlumeniG6#/%%betaG%'omega0GF%" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "limit(x(t), omega0 = beta);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 82 "eq := diff(x(t),t,t)+2*beta*diff(x(t),t) \n      + omega0^2*x(
t)=F0/m*sin(omega*t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "so
l := dsolve(eq,x(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "as
sign(sol);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "simplify(eq);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "x(t):='x(t)';" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "sol := dsolve(\{eq,x(0)=x0,D
(x)(0)=v0\},x(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "assig
n(collect(%,F0,simplify));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
5 "x(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "v1:=eval(x(t), \+
\{m=1, F0=1, beta=0.1, omega=1, omega0=1\});" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 124 "plot([eval(v1,\{x0=cos(0),v0=sin(0)\}), eval(v1
,\{x0=cos(Pi/3),v0=sin(Pi/3)\}), eval(v1,\{x0=cos(Pi/4),v0=sin(Pi/4)\}
)],t=0..100);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "v:=diff(x(
t),t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "K:=1/2*m*v^2;" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "U:=1/2*m*(omega0*x(t))^2;" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "En:=unapply(Re(K+U), t, x
0, v0, m, omega0, beta, F0, omega);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 54 "En2 := (t,beta,omega) -> En(t,0,0, 1,1,beta, 1,omega)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "plot(\{En2(t,1/10,0.5)
, En2(t,1/10,0.9), En2(t,1/10,1.0)\}, t=0..10/(1/10));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "plot3d(En2(t,1/10,omega),t=0..30,o
mega=0..2, \n    grid=[60,40], axes=frame,orientation=[-60,60],view=0.
.12);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "T:=2*Pi/omega;" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "i1 := eval(int(v*F0*sin(ome
ga*t),t=t0..t0+T)/T, \n           \{x0=0, v0=0, m=1, omega0=1, F0=1\})
;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "AvgPowe
r := unapply(i1, t0,beta,omega):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "P0 := (beta,omega) -> Re(AvgPower(0,beta,omega)):" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "Pss := (beta,omega) -> Re(A
vgPower(10/beta,beta,omega)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 48 "plot(\{P0(0.1,omega),Pss(0.1,omega)\},omega=0..4);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "plot(\{Pss(0.1,omega),Pss(0.25,omeg
a),Pss(0.5,omega)\}, omega=0..4);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "65" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
{PAGENUMBERS 0 1 2 33 1 1 }