Simple harmonic motion energy conservation problem

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The discussion revolves around a problem involving a mass m oscillating on a spring, where the maximum kinetic energy needs to be determined. The user initially calculated the spring constant k and attempted to find the change in energy but arrived at an incorrect result. It was pointed out that an additional form of potential energy must be considered due to the vertical motion of the mass. After receiving clarification, the user expressed gratitude for the assistance and acknowledged a mix-up in posting the question. The conversation highlights the importance of accounting for all forces and energy forms in oscillatory motion problems.
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Homework Statement


A mass m hanging on a spring oscillates vertically. If the equilibrium point of the oscillation is a distance d below the relaxed length of the spring and if the amplitude of the oscillation is A, what is the maximum kinetic energy of the oscillation?2. Homework Equations

The Attempt at a Solution


I did this:
mg=kd \rightarrow k=\frac{mg}{d}
\DeltaE=\frac{1}{2}k(A+d)^{2}-\frac{1}{2}kd^{2}=\frac{1}{2}\frac{mg}{d}(A^{2}+2Ad)
which wasn't the answer, but i don't know where i went wrong.
if anyone could point out the problem, i'd really appreciate your help
 
Last edited:
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There's another form of potential energy that needs to be taken into account.
 
TSny said:
There's another form of potential energy that needs to be taken into account.

which is?
 
Note that the mass is moving vertically. Think about all of the forces acting on the mass.
 
Thank you very much, TSny, for your help, I get it now.
and this question wasn't supposed to have been posted here, sorry for the mix up.
 
Thread 'Correct statement about size of wire to produce larger extension'
The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...

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