Finding x values for y=0

Hi!

I have a funtion Vprime(theta), as you can see in the graph and defined in the code below.

Im looking for a method to get all the values for theta when Vprime=0. When i use find it only returns "1" but from the graph I know that there are like 20+ values where Vprime=0.

 syms theta
V=0.5*k*l^2*sin(theta).^2+0.5*m*g*l*cos(theta) %my function;
Vprime=diff(V,theta) %function differentiated
theta=linspace(0,90,200);
Vprime=750.*cos(theta).*sin(theta) - (1473.*sin(theta))/4;
figure; plot(theta,Vprime)
find(Vprime==0)

Answer 1

[dpb]

"from the graph I know that there are like 20+ values where Vprime=0."

NO! You don't know that at all; what the graph shows is that there are a number of zero-crossings. That doesn't mean there's a value in the computed Vprime that's zero...

>> s=sign(Vprime);  % keep the sign only
>> s(s==0)=1;       % fixup the zeros (+0)
>> d=[0 diff(s)];
>> ix=find(abs(d)==2);   % find the crossings 
>> [Vprime(ix-1).' Vprime(ix).']  % show the results...
ans =
   74.9148 -204.1960
 -436.0735   27.0945
  167.6913  -93.1383
 -126.2931   18.4546
  ...
   43.9111 -135.3820
  -81.2379   81.3830
  135.3234  -44.2028
>>

Observe many crossings but no values even very close to zero, what more precisely zero (excepting the origin).

You can use interpolate to find an estimate for what the theta values would between these locations or use fsolve similarly.