Curve fitting of a damped harmonic oscillator

In summary, the conversation discusses finding a general method for fitting a function to a set of data for a damped harmonic oscillator experiment. The speaker mentions using a torsion balance with a mirror and small lead balls to calculate the gravitational constant with a high accuracy. However, their professor wanted a visual representation of the oscillation which the speaker was not able to provide. They then ask if it is possible to generate a function of the form sin(at)e^-bt to fit the data.
  • #1
Liquidxlax
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Homework Statement



I was wondering if there was a general method for finding a function that fits a set of data for a damped harmonic oscillator

I'm currently writing up a presentation on the experiment for the gravitational constant and the way i did the experiment was to use a torsion balance with a mirror at the center that oscillates with small lead balls a distance b from the mirror.

I managed to calculate the gravitational constant with in .05% of it's given value. Problem is that i think my prof wanted a visual representation of the oscillation. While my method was just to view the end points of the oscillation which is generally all you need as i have acquired such a good value.

Pictures are usually better than words, so what i have Origin is a pain sorry

tPQ1E.jpg


what I'm asking is if i could generate a function to fit this of the form sin(at)e^-bt

such that

Step_response_for_two-pole_feedback_amplifier.PNG

Homework Equations


The Attempt at a Solution

 
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  • #2
The formatting of your post went nuts, is the picture really big, can you edit?
 

Related to Curve fitting of a damped harmonic oscillator

What is a damped harmonic oscillator?

A damped harmonic oscillator is a system that exhibits periodic motion, such as a swinging pendulum or a vibrating spring, but also experiences a dissipative force that gradually reduces the amplitude of the motion.

Why is curve fitting important in studying damped harmonic oscillators?

Curve fitting is important in studying damped harmonic oscillators because it allows us to determine the parameters that describe the behavior of the system. These parameters, such as the damping coefficient and natural frequency, are essential in understanding and predicting the motion of the oscillator.

What methods can be used for curve fitting of a damped harmonic oscillator?

There are several methods that can be used for curve fitting of a damped harmonic oscillator, such as the least squares method, the gradient descent method, and the Gauss-Newton method. Each method has its own advantages and limitations, and the choice of method depends on the specific characteristics of the data and the goals of the analysis.

How can we determine the accuracy of a curve fitting model for a damped harmonic oscillator?

The accuracy of a curve fitting model for a damped harmonic oscillator can be determined by comparing the model's predictions to the actual data. This can be done by calculating metrics such as the root-mean-square error or the coefficient of determination, which measure the overall fit of the model to the data.

What are some common challenges in curve fitting of damped harmonic oscillators?

Some common challenges in curve fitting of damped harmonic oscillators include dealing with noisy data, choosing an appropriate model that accurately represents the system, and selecting the best method for curve fitting. Additionally, physical limitations, such as the non-ideal behavior of real-world systems, can also pose challenges in accurately fitting a damped harmonic oscillator model to the data.

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