Equation for a DC motor driving an arm

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YinSan
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Homework Statement
Develop dynamic equations of the system with ia(t).
Relevant Equations
Tm=KiIa
https://d2vlcm61l7u1fs.cloudfront.net/media/9b2/9b24aa39-e135-4529-9eaf-29a3cd057502/phpubWKNH.png
Untitled1.png
 
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Welcome to the PF. :smile:

It would help if you would put into words what the problem is and what your approach is.

And could you please clarify why ##\theta_m## and ##\theta_L## are not equal? I don't see any sort of gearbox that will gear down the motor to make the arm rotate differently from the shaft.

1594651927636.png
 
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K is the torsional spring constant
B = viscous-friction coefficient of shaft
between the motor and arm
TL is the disturbance on the torque arm.
K& B I think it should be located between the arm and motor. Subscript m refers to the motor. Subscript L refers to the load.
The picture I posted is my attempted solution for differential equations. I just don't know how to develop dynamic equations.