Finding oscillation of SHM of this rod, mass and spring

[aftersloth2139]

Homework Statement

Find the period of this SHM, the mass of the rod is negligible, the mass of the sphere isn't.

Relevant Equations

None

https://ibb.co/QYk8wnD

 

[aftersloth2139]

These are my notes, i already watched some yt videos but i dont seem to find the answer.

 

[berkeman]

Welcome to PF.

Can you describe in words what you are trying to do in your notes? How would you find the oscillation period if the system were simpler, like a single mass hanging from the ceiling by a spring?

(I will also send you a message with some tips for how to post math equations at PF using LaTeX).

 

[haruspex]

Remember that you are interested in oscillation about equilibrium. At equilibrium the spring is not relaxed. When you take that into account you should find that g is irrelevant.

 

[aftersloth2139]

Welcome to PF.

Can you describe in words what you are trying to do in your notes? How would you find the oscillation period if the system were simpler, like a single mass hanging from the ceiling by a spring?

(I will also send you a message with some tips for how to post math equations at PF using LaTe

Normally i would just use T=2*Pi/omega.

 

[berkeman]

Normally i would just use T=2*Pi/omega.

And how would you derive that (please show the math using LaTeX)...?

 

[aftersloth2139]

can you just help me please

 

[berkeman]

We are trying to help. We are not allowed to give answers or do your work for you here. You must do the bulk of the work. Please answer the questions above to help you get farther along in this problem.

 

[haruspex]

can you just help me please

Did you understand post #4?

 

[aftersloth2139]

And how would you derive that (please show the math using LaTeX)...?

First i wrote down the forces while at equilibrium, then i wrote down what would happen if the rod would get an acceleration.\[T = 2\pi \sqrt{\frac{m}{k}}\]. I also used a=-omega^2*x

 

[BvU]

The question you choose not to answer was

Did you understand post #4?

First i wrote down the forces while at equilibrium,

We can not see what you wrote, so helping you is nearly impossible.

then i wrote down what would happen if the rod would get an acceleration.$\left [ T = 2\pi \sqrt{\frac{m}{k}}\right ].$

We do not see it.
Where does this equation for $T$ come from ? Why do you think it applies here ?

I also used $a=-\omega^2*x$

What is each of these variables ? Do you make them up, calculate them from something else ?

Again, we do not see what you actually do, so helping is impossible.

$\$

 

[vela]

First i wrote down the forces while at equilibrium, then i wrote down what would happen if the rod would get an acceleration.\[T = 2\pi \sqrt{\frac{m}{k}}\]. I also used a=-omega^2*x

Describing your work isn't very helpful. You may think you did everything correctly, but it's quite likely you made mistakes. We can't help unless we see your actual work.

In the image you posted, there's an obvious mistake in the equation of motion. For all we know, it's still there in your work now. Not very helpful for me to simply describe that you made a mistake, is it?

It looks like you may also have a sign error in the equation. What direction, clockwise or counter-clockwise, are you considering the positive direction?

You are approaching the problem the way I would do it: write down the equation of motion to eventually get to the SHM differential equation. Then you can simply read off $\omega$ and use it to find $T$. But first you need to get the equation of motion right.