Solve Mass Using Spring & Oscillation

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The discussion revolves around calculating an astronaut's mass using a spring oscillation method in space. The astronaut is attached to a spring with a known spring constant of 240 N/m and is displaced 0.8 meters from the equilibrium position. The force exerted by the spring is calculated using Hooke's Law, resulting in a force of 208 N. This force is then equated to the weight (mg) to find the mass, yielding approximately 21.22 kg. The participant expresses uncertainty about their approach and seeks clarification on the correct method for solving the problem.
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Homework Statement



Astronauts in space cannot weigh themselves by standing on a bathroom scale. Instead, they determine their mass by oscillating on a large spring. Suppose an astronaut attaches one end of a large spring to her belt and the other end to a hook on the wall of the space capsule. A fellow astronaut then pulls her away from the wall and releases her. The spring's length as a function of time is shown in the figure

http://session.masteringphysics.com/problemAsset/1073872/3/knight_Figure_14_36.jpg
What is her mass if the spring constant is 240N/m

Homework Equations



Hookes Law
F = -kx
U = (1/2)*k*x2

The Attempt at a Solution



So the spring was pulled back 1.4 metres and then released where it went to the point 0.6
so 0.6 is the point at equilibrium, so -0.8 is the displacement and that is the x

F = (240 * 0.8)
and then I am not sure what to do, I am not even sure if I am doing this right and help would be appreciated
 
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im pretty sure my approach is wrong...

F = -260 * -0.8 = 208N

mg = weight

208/9.8 = m

m = 21.224489795918367346938775510204kg

im sure that's wrong is there a better way to approach this problem and why is the way I am approaching it wrong?
 

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