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I would like to know how the string deforms over time as it is pulled from that point (orange). Does the end closest to the pulling force move first and straighten up, wrapping around the object 'A' early on, or does the whole string change shape continuously? For a better understanding, Take a look at this figure( I've modified the diagram in order to ...

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While it is slack it will depend on the type of string and the transmission of forces. There will be an impulse propagating across the string starting from the left , there might be rotational energy while it is slack. Think of the molecules composing the string, they transmit the force to their neighbor. Once it tightens it will depend on the actual ...

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Say the density of the string is $\mu$ and the tension is $T$. It's clear that the kinetic energy of an infinitesimal piece of string is $$dT = \frac{1}{2} (\mu \, dx) u_t(x)^2$$ The length of the infinitesimal piece of string from $(x, u(x))$ to $(x + dx, u(x + dx))$ is \begin{align} d\ell &= \sqrt{dx^2 + (u(x+dx) - u(x))^2} \\ &= \sqrt{dx^2 + ...

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