Dyanimcs problem. find the dustance traveled using of a cart

[baileypatrick8]

Homework Statement

The system is released from rest with no slack in the cable and with the spring stretched 200mm. Determine the distance s traveled by the 10kg cat before it comes to rest (a) if m approaches zero and (b) if m = 2kg. Assume no mechanical interference.
Mass of cart = 10kg, k = 125 the spring starts stretched .2m

Homework Equations

I have attached a picture of the problem n as well as my attempt at solving it.

The Attempt at a Solution

I assumed the work of the cart would equal that of the spring. I found the acceleration of the cart is twice that of the spring through f = ma I got
10kg (g) sin25 - T = mAx

And in the y firection for the spring assumed the force of the spring down is equal to twice that of T with Fs = 125/2 (.2^2 -(.2-d)^2)

From here I tried set ting the work of each equal to each other and integrating and got the wrong answer.

 

[SteamKing]

Your file is damaged and cannot be opened.

 

[baileypatrick8]

I hope it worked this time. The preview showed up fine on my end