Çözüldü Conservation of Energy - Spring Mechanics - Trigonometry

A GRE Physics adaptation from Eskişehir Technical University:

At some place where the gravitational acceleration is g (meter per squared second), if a block of mass m (kg) is attached to a compressed string whose spring constant is k (Newton per meter) and which is fixed on the bottom of a frictionless inclined plane that has an angle of θ (radians) and which has the compression amount of x (cm), which of the following equations is the distance (in meters) covered by the released block from rest until it stops relative to its original position on the inclined plane?

A) (1 / 2)·10^(-4)·k·x^2·sin(θ) / (m·g)
B) (1 / 2)·10^(-4)·k·x^2·cos(θ) / (m·g)
C) 10^(-4)·k·x^2·sec(θ) / (m·g)
D) 5·10^(-5)·m·g·cot(θ) / (k·x^2)
E) 5·10^(-5)·k·x^2·csc(θ) / (m·g)


https://i.ibb.co/mvyhDPY/ETU.png

Length = 0.5·k·x^2·10^(-4)·csc(θ) / (m·g)
Length = 5·10^(-5)·k·x^2·csc(θ) / (m·g).

Original Question and Solution:

https://i.ibb.co/bd0R1Z0/ETU2.png
https://fizik.eskisehir.edu.tr/Uploads/fizik/files/FIZ105_MidtermII_2022-2023.pdf
(Page 4, Question 11)

Note: A typo in the original solution has been corrected.
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The comment from https://chat.openai.com/ on the adapted version:

The question is grammatically correct, but it is quite complex and technical, which might make it challenging for some readers to understand immediately. To enhance clarity, you could consider breaking it down into smaller, more digestible parts or providing additional context. Here's a slightly simplified version:

"In a scenario where the gravitational acceleration is 'g' (m/s²), a block with mass 'm' (kg) is connected to a compressed spring with spring constant 'k' (N/m). The spring is attached to the bottom of a frictionless inclined plane with an angle 'θ' (radians) and is compressed by an amount 'x' (cm). When the block is released from rest, how far will it travel along the inclined plane before coming to a stop, relative to its original position? Choose the equation that accurately calculates this distance in meters."

By breaking down the information and using more concise language, you can make the question more approachable for readers while still maintaining its technical accuracy.