Looking for some help realting to spring energy changes

[Jonah765]

Homework Statement

https://imgur.com/gallery/PQx8SmX

Homework Equations

EPE (elastic potential energy) = 1/2kx^2

GPE (gravitational potential energy) = mgh

The Attempt at a Solution

my attempt, https://imgur.com/gallery/lJDhwqD
[/B]
I feel like I've made progress considering the quadratic factored to a neat 0.05 m, however from there i don't know how to proceed to find the maximum height. Essentially all that is required is to find the value of h, then max height = x + h, but I am not sure how to go about that

Perhaps i am going about this the wrong way, I have tried to consider the change in energy from stage 2 to 3, but come to the same final result/dilemma. any help is appreciated, ty.

 

[Np14]

Please upload an image.

 

[Jonah765]

Please upload an image.

As far as I am aware I have, there are two imgur links in my post, unless you mean something else? :)

 

[Orodruin]

As far as I am aware I have, there are two imgur links in my post, unless you mean something else? :)

That is not uploading them, that is giving external links that gives the people you are asking for help an additional barrier to helping you since they have to open an external page. You should include the images in your post.

You should also read the homework rules regarding uploading problem statements and attempts in image format.

 

[haruspex]

Perhaps i am going about this the wrong way

I think you have misunderstood the set-up. My reading is that the spring is merely hooked onto something at the top end so that when released the entire spring flies up to some height.
Also, I think you have to take a rather simplistic view, converting all the spring energy into height gain. In reality, massive springs are complicated; some of the energy would go into internal vibrations.