One last thing. Since some of the eigenvalues have complex parts, should I just take the real part of the function Re(\omega_{2}) and proceed with the usual standard error propagation?
Suppose I have some observables \alpha, \beta, \gamma whose central values and uncertainties \sigma_{\alpha}, \sigma_{\beta}, \sigma_{\gamma} are known.
Define a function f(\alpha, \beta, \gamma) which has both real and complex parts. How do I do standard error propagation when imaginary...
I was initially thinking of "brute forcing" my experimental values for (k_{1},k_{2},k_{3}) as you said. It really does seem like a sufficiently good approximation for the uncertainty. However, I want to be as formal as possible with everything, especially error propagation. It may be the last...
I found \omega_{1}, \omega_{2}, \omega_{3} through a nifty WolframAlpha widget. I set x=k1, y=k2, and z=k3. As you can see from the equation of just one eigenvalue, I don't think that is easily differentiated. Is this the only correct way to do uncertainty propagation? If yes, what software...
So you are saying that $$\omega _{1}(k_{1}, k_{2}, k_{3}) = \sqrt{\frac{k_{1}}{m}} + \sqrt{\frac{k_{2}}{m}} + \sqrt{\frac{k_{3}}{m}}$$, right? Again, I assume that $$m_{1} = m_{2} = m_{3} = m$$. I also solved for the eigenvalue problem through MatLab, so I think your formula works only if I...
I am a senior physics and mathematics major, and this is my last semester. As a result, I am taking advanced physics lab, which feels more like a grad school experiment than an undergrad. One of the labs deals with the modal analysis of three spring-mass systems placed vertically as shown in the...
I took CS 1 (simple Java stuff) on the first semester, and that was relatively easy for me to do. However, I am not doing so well in my CS2 course, as I just miserably failed one exam to the point of likely losing hope of getting a B on that course. Now, I am a physics and math major, and I am...