I want the graph to look like the left one and I want the pendulum to turn from thet$\_$in to thet$\_$out. The pendulum is run by the motor so that it could turn, but i$\text{'}$m not sure why it is not working as expected $($the graph produimport numpy as np

import matplotlib.pyplot as plt

from scipy.integrate import solve$\_$ivp

from Pendulum$\_$Animations import animate$\_$pendulum

#Known parameters

g $=9\mathrm{.}81$ #m$/$s$^2$

L $=1\mathrm{.}2$ #m

m $=20$#kg

thet$\_$in $=120*($np$.$pi $/180)$ #starting angle of mechanism $($rad$)$

thet$\_$out $=210*($np$.$pi $/180)$ #Finishing angle $($rad$)$

#Motor constants

T$\_$s $=0\mathrm{.}69$ #Stall Torque, FROM CATALOGUE $($Nm$)$

omega$\_$m $=2750*(2*$ np$.$pi$/60)$ #No load angular speed $($rad$/$s$)$

k $=$ T$\_$s $/$ omega$\_$m #motor gradient constant

#Range of gear ratios to try

#G$\_$r $=[295\mathrm{.}503]$

G$\_$r $=[320]$

#Equation of motion $($of a pendulum$)$

def f$\_$new$($t$,$z$,$ vr$)$:

def f$($t$,$ z$)$:

theta $=$ z$[0]$

omega $=$ z$[1]$

if theta$$ thet$\_$out:

T$\_$m $=$ vr $*$ k $*($thet$\_$out $-$ theta$)$ #motor torque

elif theta $>$ thet$\_$in:

T$\_$m $=$ vr $*$ k $*($thet$\_$in $-$ theta$)$

else:

T$\_$m $=0$

alpha $=($T$\_$m $+($m$*$g$*$L$*$np$.$sin$($theta$)))/($m$*$L$**2)$ #$+$ so will rotate upwards

dz $=[$omega$,$ alpha$]$

return dz

return f$($t$,$ z$)$

#Creating events function $($to terminate exactly where we specificy$)$

def my$\_$event$($t$,$z$,$ vr$)$:#t $=$ time, z $=$ state $($displacement$)$

return z$[0]-$ np$.$pi$/2$ #returns the first state $($displacement$)$

my$\_$event.terminal $=$ True #solve$\_$ivp will stop when this condition is met

my$\_$event.direction $=+1$ #controls the way in which the evnt is triggered

#the event will only trigger when the event function output reaches zero in a positive direction

#Solver parameters

T $=8$ #Time for it to run for $($s$)$

IC $=[$thet$\_$in$,0]$ # Initial conditions $($position in angle, velocity$)$

t$\_$out $=[]$ #time array

z$\_$out $=[]$ #data array $[$position$,$ velocity$]$

#Solvers

for i in range$($len$($G$\_$r$))$:

vr $=$ G$\_$r$[$i$]$ #iterate ranges of gear ratios

sol $=$ solve$\_$ivp$($f$\_$new, $(0,$T$),$ IC$,$ rtol $=1$e$-4,$ max$\_$step $=1$e$-2,$ args $=($vr$,),$ events $=$ my$\_$event$)$

t $=$ sol.t

z $=$ sol.y

t$\_$out.append$($t$)$

z$\_$out.append$($z$)$

#animate

animate $=$ True #will only animate when its true

#thet$\_$gr

if animate $==$ True:

thet $=$ z$\_$out$[-1]$

ani $=$ animate$\_$pendulum$($t$\_$out$[-1],$ thet$[0,$:$])$

#Plots

fig, ax$1=$ plt$.$subplots$(2)$

for i in range$($len$($t$\_$out$))$:

ax$1[0].$plot$($t$\_$out$[$i$],$ z$\_$out$[$i$][0,$:$],$ label $=$ str$($G$\_$r$[$i$]))$

ax$1[0].$axhline$($y $=$ thet$\_$out, linestyle $=\text{'}-.\text{'},$ label $=$ 'Finishing angle', color $=$ 'red'$)$

ax$1[0].$set$\_$xlabel$(\text{'}$Time $($s$)\text{'})$

ax$1[0].$set$\_$ylabel$(\text{'}$Angle $($rad$)\text{'})$

ax$1[0].$legend$()$

#Velocity

for i in range$($len$($t$\_$out$))$:

ax$1[1].$plot$($t$\_$out$[$i$],$ z$\_$out$[$i$][1,$:$],$ label $=$ str$($G$\_$r$[$i$]))$

ax$1[1].$set$\_$xlabel$(\text{'}$Time $($s$)\text{'})$

ax$1[1].$set$\_$ylabel$(\text{'}$Velocity $($rad$/$s$)\text{'})$

ax$1[1].$legend$()$ced is not the same$).$ Here is my code: