ans the following question please;
If a uniform spring is cut in half, what is the force constant of each half? Justify your answer. How would the frequency of SHM using a half-spring differ from the frequency using the same mass and the entire energy?
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Hooke's Law is F = kx, where F = extension force, x = extension distance, k = spring constant (what you have called force constant)
Rearranging for k:
k = F/x.
The force required to stretch half a spring to the same length as the original is clearly twice (because the half spring is harder to stretch) so in the above equation k is doubled.
Frequency of SHM is twice that of the original spring because SHM frequency is proportional to k.
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