Non-dimensional differential equation 2

In summary, the conversation discusses a non-dimensional equation for the height at the highest point and asks for a determination of the time and speed of a body when it travels from the highest point to the ground, to $O(\mu)$ accuracy. However, the given information is not sufficient to make any calculations. The problem appears to be similar to other threads started by the same person.
  • #1
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.
 
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  • #2
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?
 

FAQ: Non-dimensional differential equation 2

What is a non-dimensional differential equation 2?

A non-dimensional differential equation 2 is a type of mathematical equation used to describe the relationship between two or more variables that are non-dimensional, meaning they have no units. It is typically written in the form of a differential equation, where the rate of change of one variable is dependent on the values of the other non-dimensional variables.

Why are non-dimensional differential equations 2 important in science?

Non-dimensional differential equations 2 are important in science because they allow us to study and understand complex systems that involve multiple variables. By removing units from the variables, we can focus on the underlying relationships between them and make predictions or solve problems without worrying about specific numerical values.

How do you solve a non-dimensional differential equation 2?

Solving a non-dimensional differential equation 2 involves finding a general solution that satisfies the equation for all possible values of the non-dimensional variables. This can be done using various mathematical techniques such as separation of variables, substitution, or numerical methods.

What are some real-world applications of non-dimensional differential equations 2?

Non-dimensional differential equations 2 have many applications in various fields of science and engineering. They are commonly used to model and analyze physical systems such as fluid dynamics, heat transfer, and chemical reactions. They are also used in economics, ecology, and other fields to study complex systems and make predictions.

What are the limitations of non-dimensional differential equations 2?

While non-dimensional differential equations 2 are powerful tools, they do have limitations. They may not accurately describe systems with highly non-linear or chaotic behavior. Additionally, they may not be applicable to systems with significant variations in scale or when considering extreme conditions. It is important to carefully consider the assumptions and limitations of these equations when using them in scientific research and applications.

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