Module 2 Lecture 2 - Virtual Work

[travismalave]

Had a couple questions when going through Lecture 2 of Module 2. Appreciate any help or feedback.

1. How is $\delta W$ calculated? I would assume similar to how $\delta T$ calculated that $dx/d\theta$ would be -$mgL/2sin\theta$. Or is this due to $\delta W$ being the result of the integral with respect to $\theta$ based on the definition of $\delta E$ in the variational calculus section of Lecture 1 of Module 2?
2. How does the $1/2$ drop off in the final EoM when it comes to the $F\theta$ term? I wasn't able to fully follow that logic jump.

[travismalave]

The Q&A session on 2/15 covered my questions above in case anyone else had similar questions.