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indianaronald

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In summary, the conversation discusses the possibility of obtaining complex roots in a spring-mass system when using the Laplace transform, and how these roots can be interpreted in terms of real solutions. It also mentions that a damped harmonic system can have complex conjugate roots, but these can be equivalent to real solutions when certain conditions are met.

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indianaronald

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indianaronald

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LCKurtz said:

indianaronald said:

By a "solution pair" I mean the general solution is$$

y = Ae^{at}\cos(bt)+e^{at}\sin(bt)$$Without actually seeing what your system is and what your work looks like, I can't be more specific about your problem.

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alphy

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It is important to note that the Laplace transform is a powerful mathematical tool for solving differential equations, but it is not foolproof. In some cases, it may give complex roots that do not seem possible, as you have observed in your spring-mass system. This could be due to the limitations of the Laplace transform in handling certain types of functions or initial conditions.

In such cases, it may be necessary to use other methods, such as traditional differential equation solving or numerical methods, to obtain more accurate and reliable solutions. It is also important to carefully check your input values and equations to ensure they are correct and appropriate for your system.

Additionally, keep in mind that complex roots can still be valid solutions in some cases, so it is important to thoroughly analyze and interpret the results of your Laplace transform in the context of your system. Overall, the inverse Laplace transform in Matlab is a useful tool, but it is important to understand its limitations and use it in conjunction with other methods for a comprehensive and accurate analysis.

Inverse Laplace in Matlab is a function that calculates the inverse Laplace transform of a given function or expression. The inverse Laplace transform is used to convert a function from the s-domain to the time-domain.

To use the inverse Laplace function in Matlab, you need to have the Symbolic Math Toolbox installed. Once you have this toolbox, you can use the `ilaplace`

function to calculate the inverse Laplace transform of a given function or expression.

The "iota" output in the inverse Laplace function in Matlab represents the imaginary unit, which is denoted by the letter "i". This is a common notation in mathematics and is used to represent complex numbers, which are often encountered in the s-domain.

Yes, the inverse Laplace function in Matlab can handle complex functions. However, it is important to note that the function `ilaplace`

only accepts symbolic expressions, so the complex function must be written in terms of variables such as `s`

and `t`

.

One limitation of using the inverse Laplace function in Matlab is that it may not be able to calculate the inverse Laplace transform for certain functions or expressions. This can happen when the function is too complex or when it has poles at the origin. In these cases, alternative methods may need to be used.

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