Find K: Hooke's Law & Massless Spring Homework

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SUMMARY

The discussion focuses on calculating the spring constant for a massless spring compressed to 68% of its relaxed length of 0.260 m, with a mass of 0.240 kg placed on top. The mass takes 1.60 seconds to reach the peak of its trajectory after being released. Key equations include Hooke's Law (F = -kx) and the spring potential energy formula (0.5kx²). The energy stored in the spring converts entirely into gravitational potential energy as the mass ascends.

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Homework Statement



A massless spring of length 0.260 m is in its relaxed position. It is compressed to 68.0 percent of its relaxed length, and a mass M=0.240 kg is placed on top and released from rest (shown on the right). The mass then travels vertically, taking 1.60 s to reach the top of its trajectory. Calculate the spring constant.

Homework Equations



F = -kx
Spring potential = 0.5kx^2

The Attempt at a Solution



I would prefer if someone explained the concept behind it so that I can work it out myself, rather than people just posting answers.
 
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So if the spring is compressed to 68% of its initial length, to what length is is compressed to?

Thus by how much is it compressed by?

Now they say that, it takes 1.6s to reach the top of the trajectory. So all the energy stored in the spring is converted into what sort of energy?

When you figure out that, then can you make an equation relating the energy stored to the converted energy?


(Also remember, it is only being influenced by gravity g)
 

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