Looking for some help realting to spring energy changes

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
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I feel like ive made progress considering the quadratic factored to a neat 0.05 m, however from there i dont 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 im 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.

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

Orodruin
Staff Emeritus
Homework Helper
Gold Member
As far as im 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.