Time to restore equilibrium on horizontal block spring system

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In a horizontal block-spring system on a frictionless table, the time it takes for the block to return to the equilibrium position is influenced by the spring constant (k) and the frequency of oscillation. A greater spring constant results in a higher frequency, leading to quicker oscillation and restoration times. However, if acceleration at release is due to increased displacement while keeping k constant, the relationship changes. The rank of time does not solely depend on net forces but also on the system's frequency and spring constant. Understanding these dynamics is crucial for accurately predicting the restoring time in harmonic oscillators.
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Homework Statement


I'm comparing horizontal block-spring systems on frictionless table and need to rank the time it takes for the block to return to equilibrium position. I know the rank of the net forces, so I'm wondering if the greater the acceleration, the quicker the restoring time? If so, then the rank of time would be the same as the rank of the magnitude of the forces right?
 
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bocobuff said:

Homework Statement


I'm comparing horizontal block-spring systems on frictionless table and need to rank the time it takes for the block to return to equilibrium position. I know the rank of the net forces, so I'm wondering if the greater the acceleration, the quicker the restoring time? If so, then the rank of time would be the same as the rank of the magnitude of the forces right?

Consider a simple harmonic oscillator.

It's frequency is proportional to the spring constant k.

f ∝ k

If k is greater then the frequency is greater isn't it?
And if frequency is greater ...

However if your greater acceleration at release is due to greater displacement from the equilibrium, if k is the same then ...

See also: http://en.wikipedia.org/wiki/Harmonic_oscillator#Spring-mass_system
 
Thread 'Correct statement about size of wire to produce larger extension'

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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