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Figure 1 : In before part have mass $m$ not moving then $x=0$ ,When the object is at lowest point the object will be in equilibrium, $v=0$ and object move down $x$

To find the spring constant suppose a body of mass $m$ is on a spring with the spring constant $k$
I have 2 method to find spring constant

  1. From the object in the equilibrium state so $F=kx$ that is $mg=kx$ thus $k=\frac{mg}{x}$
  2. Use energy conversation : $mgx=\frac{1}{2}kx^2$ thus $k=\frac{2mg}{x}$

Question is why k in 1. and 2. not equal? What did I do wrong?

figure 1

IamA
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1 Answers1

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There are two different $x$ s. The equilibrium $x$ is where the mass will hang unmoving, halfway between the top and the bottom (the other $x$) of the mass's up and down movement.

Peter
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