Time to restore equilibrium on horizontal block spring system

[bocobuff]

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?

 

[LowlyPion]

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