Functions that exhibit exponential decay behavior?

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SUMMARY

The discussion centers on modeling a real-life system resembling a pendulum using differential equations, specifically focusing on functions that exhibit exponential decay behavior. The participants noted that experimental data produced a decaying exponential plot, but using an exponential function for the rate of change resulted in a complex system of equations. They inquired about alternative functions that could mimic this behavior or whether to resort to a linear approximation. The consensus emphasizes the need for more specific details to provide tailored suggestions.

PREREQUISITES
  • Understanding of differential equations
  • Familiarity with exponential functions and their properties
  • Basic knowledge of data plotting and analysis
  • Experience with modeling real-life systems mathematically
NEXT STEPS
  • Research alternative functions that exhibit exponential decay, such as logarithmic or polynomial functions
  • Explore numerical methods for simplifying complex systems of equations
  • Learn about linear approximations and their applications in modeling
  • Investigate the use of software tools for data analysis and function fitting
USEFUL FOR

Students in mathematics or engineering courses, particularly those studying differential equations, as well as researchers and practitioners involved in modeling dynamic systems.

Buffel
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Any help is appreciated, thanks.

Homework Statement


In my course of differentials equations we were given the task to model a real life system with them, we choosed something that resembles a pendulum.

Homework Equations


The Attempt at a Solution


We went to the lab and got experimental data from our system and the resulting data plot looks like a decaying exponential, but using an exponential as our rate of change results in a very complicated system of equations and I was wondering if there exists any other function that exhibits the same behavior or give up and use a linear approximation.
 
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Many functions, when multiplied by an exponential function, will look similar. Without more details on your problem, it is hard to suggest anything.
 

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