Potential spring energy

[deleted388502]

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Hey guys, really simple question -

in 1/2kx^2 when we're calculating the potential energy, the X is the MAXIMUM displacement that spring can have, correct? is this just the maximum capacity that spring constant can hold? I'm just a tad confused as to how that "maximum" displacement is determined.

Thanks!

 

[MolonLabe16]

My understanding is that x only represents the displacement from the equilibrium point, but doesn't necessarily have to be the maximum amount that spring can be stretched or compressed.

For example, say a certain spring can be compressed only 5 cm, there are a whole range of potential displacements (0 < x < 5 cm) and energies that can arise from these values.

I hope this made sense and helped!

 

[deleted388502]

mmm okay, but to determine the maximum velocity, i.e. when you set it equal to 1/2mv^2, what 'x' are you using?

I guess I'm confused about how maximum displacement is determined conceptually, because when I look at this:

I'm lost as to how A is still maximum displacement even though it's near the point of origin.

 

[Cawolf]

X is generally the displacement from the equilibrium position.

The question states that B is the equilibrium position, so x = 0 when the block is at B.

A would be -x and C would be +x displacement.

 

[MolonLabe16]

mmm okay, but to determine the maximum velocity, i.e. when you set it equal to 1/2mv^2, what 'x' are you using?

I guess I'm confused about how maximum displacement is determined conceptually, because when I look at this:

I'm lost as to how A is still maximum displacement even though it's near the point of origin.

The diagram is depicting simple harmonic motion, so in this case there would be a maximum displacement x which, as @Cawolf says, is equal to the distance from A to B (and C to B), and the equilibrium point would be at point B.

@avenlea When you set 1/2 kx^2 = 1/2 mv^2, you are realizing that the max spring potential energy at maximum displacement x from equilibrium is being completely transformed into kinetic energy at x=0, which will tell us the maximum velocity. So we could calculate the maximum displacement from equilibrium given the maximum velocity of the moving mass and vice versa (assuming we also know m and k).

 

[deleted388502]

Cool beans. Looking at this a few days later made me realize I was overthinking beyond belief. Thanks guys.