Manipulate[
Animate[
Show[{
Plot[{
A1 f[π z]Cos[α π t]+A2 f[2π z]Cos[2α π t]+A3 f[3π z]Cos[3α π t]+A4 f[4π z]Cos[4α π t]+A5 f[5π z]Cos[5α π t]
}/.{α->1}
,{z,0,1},PlotRange->{-3,3},Axes->False],
Graphics[
{
Point[{1,0}],
Point[{0,0}]
}
]}],
{t,0,∞},AnimationRunning->True
],
Item[Style["Stojaté vlny",Bold,14],Alignment->Center],
Delimiter,
{{f,Sin,"F((Subscript[k, m])z) = "},{Sin->"Sin((Subscript[k, m])z) - pevné konce",Cos->"Cos((Subscript[k, m])z) - volné konce"}},
Delimiter,
Item[Style["(∑_(m = 1)^5)(Subscript[A, m]) F((Subscript[k, m])z) cos((Subscript[ω, m])t)"],Alignment->Center],
Item["(Subscript[k, m]) = (π/L)m   (Subscript[ω, m]) = (Sqrt[(T/ρ)])(Subscript[k, m])",Alignment->Center],
Delimiter,
{{A1,1,(Subscript[A, 1])},0,1},{{A2,0,(Subscript[A, 2])},0,1},{{A3,0,(Subscript[A, 3])},0,1},{{A4,0,(Subscript[A, 4])},0,1},{{A5,0,(Subscript[A, 5])},0,1},
Delimiter,
Row[{
Button["1. mód",{A1=1,A2=0,A3=0,A4=0,A5=0}],
Button["2. mód",{A1=0,A2=1,A3=0,A4=0,A5=0}],
Button["1. a 2. mód",{A1=1,A2=1,A3=0,A4=0,A5=0}],
Button["Amplitudy 1/(2^m)",{A1=1,A2=1/2,A3=1/4,A4=1/8,A5=1/16}],
}],
ControlPlacement->Left
]