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{SECT 0 {EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 20 "Harmonicky oscilator
" }}{PARA 0 "" 0 "" {TEXT -1 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 "assign(so
l);" }}}{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 := simplify(eva
l(E, omega0=sqrt(k/m)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 
"eq1 := A*cos(omega0*t + theta) = x(t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "eq2 := eval(eq1, t=0);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 34 "eq3 := eval(eq1, t=Pi/(2*omega0));" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 28 "solve(\{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 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 14 "Fazovy portret
" }}}{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 := unapply
(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 harmonicky poh
yb" }{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 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {MPLTEXT 
0 21 34 "Oscilator buzeny harmonickou silou" }}}{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)=F
0/m*sin(omega*t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "sol :=
 dsolve(eq,x(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "assign
(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 "assign(colle
ct(%,F0,simplify));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "x(t);
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {MPLTEXT 
0 21 26 "Energie, vykon a rezonance" }}}{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, x0, v0, m, omega0, beta, F0, \+
omega);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 121 "plot(\{En(t,0,0
, 1,1,1/10, 1,0.5), \n      En(t,0,0, 1,1,1/10, 1,0.9), \n      En(t,0
,0, 1,1,1/10, 1,1.0)\}, t=0..10/(1/10));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 119 "plot3d(En(t,0,0, 1,1,1/10, 1,omega),t=0..30,omega=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(omeg
a*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 38 "AvgPower
 := 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(AvgPower(
10/beta,beta,omega)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "pl
ot(\{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,omega),Pss(0.5
,omega)\}, omega=0..4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}}{MARK "56" 0 }{VIEWOPTS 1 1 0 1 1 1803 }