Can sombody explain how to calculate \frac{d}{dt}(x + lsin(\theta)) for example? I don’t understand how the time derivatives simplify to equation 22.

Like how is \frac{d}{dt}(c\dot{x}) = \ddot{cx}

Can sombody explain how to calculate \frac{d}{dt}(x + lsin(\theta)) for example? I don’t understand how the time derivatives simplify to equation 22.

Like how is \frac{d}{dt}(c\dot{x}) = \ddot{cx}

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Maybe I don’t understand your question. Are you asking about the constant rule in differentiation?

\ell is a constant, probably the length of the pendulum.

\frac{d}{dt}(x+\ell\sin\theta) = \frac{d}{dt}(x) + \frac{d}{dt}(\ell\sin\theta) = \dot{x} + \ell\frac{d}{dt}(\sin\theta) = \dot{x} + \ell\dot{\theta}\cos\theta

Don’t forget this term is squared in the equation.

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