Help Coupled harmonic oscillators.

[musicality213]

Homework Statement

I am working on my lab, in which I have to find eigenvalues of coupled harmonic oscillators running a) in the same direction and b) in opposite directions. Two masses, three springs.

--v^V^V^V^v--[M]--v^V^V^V^v--[M]--v^V^V^V^v-

I have to compare my calculated values to measured values. My three trials for the same-direction oscillation came back with an average frequency of 0.901 Hz. Each of the carts have mass M, 0.25 kg. I calculated the outer springs as having values of k of 35.28 Nm each, and the center spring as having a constant of 80.18 Nm.

I'm having a lot of trouble getting my measured and calculated frequencies to the same order of magnitude, let alone the same number.

I'm assuming w₁ and w₂ (the frequencies of each cart) should be the same, right?

Homework Equations

F=ma=kx
w=sqrt(k/m)
?

The Attempt at a Solution

Calculated frequency: 0.918 +/- 0.051 Hz (three trial average)

Assuming k=35.28 for the outer springs and the mass of each cart is 0.25 kg:

w = (35.28)/(0.25), except for it's not.

I really have a poor understanding of this, and I need help. I really appreciate it.

 

[anathema]

Thank you for your post. It seems like you are working on a challenging lab and have put a lot of effort into your calculations so far. I understand the frustration of not being able to match calculated and measured values. However, it is important to remember that there are often many factors that can affect the accuracy of our calculations and measurements.

In order to better assist you, could you provide more information about your experimental setup and procedures? What methods did you use to measure the frequencies? Are there any potential sources of error in your measurements? Also, have you considered any other factors that could affect the frequencies, such as damping or non-ideal behavior of the springs?

In terms of your question about the frequencies being the same for both carts, it is not necessarily the case that they should be exactly the same. In fact, the frequencies may be slightly different due to subtle differences in the masses or stiffness of the springs. However, they should be in the same order of magnitude.

I would recommend reviewing your calculations and experimental setup carefully, and also seeking help from your instructor or a lab partner. Sometimes having a second set of eyes can help identify any errors or factors that may have been overlooked.

I wish you luck in your lab and hope you are able to resolve the discrepancies between your calculated and measured values. Keep up the good work!

 

[kerimek]

Hello,

It looks like you are working on a lab involving coupled harmonic oscillators. This can be a complex topic, so it's understandable that you are having trouble getting your calculated and measured frequencies to match up. First, let's address your question about the frequencies of each cart. In the case of coupled oscillators moving in the same direction, the frequencies of each cart will be the same. This is because they are connected by the springs and will move together as one system.

Now, onto your calculations. It seems like you have correctly identified the relevant equations for this system, including F=ma and w=sqrt(k/m). However, I am not sure where you are getting the values for k and m that you are using in your calculations. It would be helpful to see your work and the specific values you are using so that I can provide more specific guidance.

In general, when working with coupled oscillators, it is important to consider the forces and displacements of each individual mass, as well as the forces and displacements of the entire system. It may also be helpful to review the concept of normal modes, which can help you understand the behavior of coupled oscillators.

I hope this helps and good luck with your lab!