Phase diagram for a plane pendulum

Questions
1

I’m having a problem trying to plot a phase diagram for a plane pendulum. For some reason the function I created will not plot. if I solve for specific variable it will give me a solution but anything else I do with it will not work (Manipulate[], Plot[], etc..). Can someone help me out?

thetadot[m_, g_, l_, \[Theta]_, \[Theta]max_] := 
  2 Sqrt[(g/l)[Sin[\[Theta]max/2]^2 - Sin[\[Theta]/2]^2]];

Manipulate[
 Plot[thetadot[20, 10, 1, \[Theta], \[Theta]max], {\[Theta], -2 Pi, 
   2 Pi}], {\[Theta]max, 0, 2 Pi}]
2

You are using [Sin[[Theta]max/2]^2 - Sin[[Theta]/2]^2] to group those two things together and Mathematica does not instantly put giant red bouncing pointing fingers pointing at that [ and ] to say that is unacceptable. Change those [ and ] to ( and ), but only in the one place where you are using those to group, not in the other places where you are correctly using these around function arguments, then run the code and slide the slider and see your plot

3

Remove incorrect [ ] and everything works

thetadot[m_, g_, l_, \[Theta]_, \[Theta]max_] := 
  2 Sqrt[(g/l) Sin[\[Theta]max/2]^2 - Sin[\[Theta]/2]^2];

Manipulate[
 Plot[thetadot[20, 10, 1, \[Theta], \[Theta]max], {\[Theta], -2 Pi, 
   2 Pi}], {\[Theta]max, 0, 2 Pi}]
4

Thank you both! it worked out beautifully.

Cheers,
Dev