Question about an equation of kinematics derived with Lagrangian Mechanics

Question

In this video https://youtu.be/2o3-GTk72x8, Professor Michel Biezen derives the following equation :
$$mx’’+mell left(theta’’ cos(theta)-sin(theta)(theta’)^2right) = -kx. $$
However, the terms inside the bracket are not dimensionally equal (the coefficient of $sin(theta)$ is not dimensionally equal to Force), so there must be some error in this equation. I cannot figure out exactly where the error as but my best guess is the error comes in after applying the product rule right before this equation is written at 3:47

J. Murray · Answer

$theta$ is dimensionless, so all the units in that equation are correct. In particular, the dimensions of $theta’’$ and $(theta’)^2$ are both $T^{-2}$.

Paulo Mourão · Answer

It is dimensionally correct.
$theta$ and $sin(theta)$ are dimensionless, so $dot{theta}$ has dimensions of $T^{-1}$ and $(dot{theta})^2$ has dimensions of $T^{-2}$. Combine this with the $m l$ outside the parenthesis, you get $kgcdot mcdot s^{-2}$, which is the unit for Force

Question about an equation of kinematics derived with Lagrangian Mechanics

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