Non-dimensional differential equation 2

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SUMMARY

The discussion centers on solving a non-dimensional differential equation for the height of a body at its peak, represented by the equation h(μ) = (1/μ) - (1/μ²) log_e(1+μ) for 0 < μ << 1. Participants emphasize the need for additional information to determine the non-dimensional time for the body to descend from the highest point to the ground and to estimate its speed upon return. The conversation also notes similarities to previous threads, suggesting a recurring theme in the user's inquiries.

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ra_forever8
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Consider non-dimensional equation for the height at the highest point is given by
\begin{equation} h(\mu)= \frac{1}{\mu}- \frac{1}{\mu^2} \log_e(1+\mu) \end{equation}
$0<\mu\ll 1.$
Determine to $O(\mu)$, the (non-dimensional) time for the body to travel from the highest point to the ground, and determine an estimate for the (non-dimensional) speed of the body when it returns to the ground, again to $O(\mu)$.

=> I really don't how to start this question. please help me.
 
Last edited:
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grandy said:
Consider non-dimensional equation for the height at the highest point is given by
\begin{equation} h(\mu)= \frac{1}{\mu}- \frac{1}{\mu^2} \log_e(1+\mu) \end{equation}
$0<\mu\ll 1.$
Determine to $O(\mu)$, the (non-dimensional) time for the body to travel from the highest point to the ground, and determine an estimate for the (non-dimensional) speed of the body when it returns to the ground, again to $O(\mu)$.

=> I really don't how to start this question. please help me.

You do not have enough information to say anything about the time.
Is there some information missing from the problem statement?

Btw, this problem looks *a lot* like 2 other threads you started.
Are they perhaps all about the same problem?
 

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