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

 

[thomate1]

I would approach this question by first clarifying the definitions of equilibrium and restoring time in the context of a horizontal block-spring system. Equilibrium refers to a state where the net force on the block is zero, meaning that the block is not accelerating or moving. Restoring time, on the other hand, refers to the time it takes for the block to return to its equilibrium position after being displaced.

In this system, the restoring force is provided by the spring, which is directly proportional to the displacement of the block from its equilibrium position. Therefore, the greater the displacement, the greater the restoring force and the quicker the block will return to equilibrium. This means that in general, a larger acceleration will result in a shorter restoring time.

However, it is important to note that the acceleration of the block also depends on the mass of the block and the stiffness of the spring. So while a larger acceleration may result in a shorter restoring time, it is not the only factor that determines the restoring time.

Additionally, the rank of the net forces does not necessarily correspond to the rank of the magnitude of the forces. The net force is the sum of all the forces acting on the block, while the magnitude of the forces refers to the individual forces themselves. So the rank of the net forces may not necessarily be the same as the rank of the magnitude of the forces.

In conclusion, the time it takes for a horizontal block-spring system to return to equilibrium depends on various factors such as the displacement, mass, and stiffness of the system. While a larger acceleration may result in a shorter restoring time, it is not the only factor that affects the restoring time.