I want to create a code that will satisfy the equation of motion for the pendulum. The pendulum will rotate with the support of a motor. At first, the pendulum will be at the position of thet$\_$in and it will end at the position of thet$\_$out. Please can you fix the equation of motion so that it will wor as expected:

import 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$($t$,$z$)$:

theta $=$ z$[0]$

omega $=$ z$[1]$

if theta $$ thet$\_$out and omega $>0$:

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

else:

T$\_$m $=0$

dz $=[$ omega,

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

return dz