00:03
Okay, so we have here a kind of an investigation driven question where you had to kind of like investigate relationships dealing with simple harmonic motion, mass on a spring, and the friction is horrid, i'm sorry, the surface is horizontal and frictionless.
00:22
So we, by being frictionless, we don't have a loss of energy due to some external force acting on the system through friction.
00:29
So that's nice.
00:30
That means all of our energy is going to, going to be at least, it looks the way that it looks based on the problem.
00:36
It's going to be conserved.
00:38
So we do know that for this problem, energy, let's just say because no friction, total mechanical energy is conserved.
01:07
Speaking about energy while we're on it, the only two forms of energy we actually have, is going to be really just either kinetic energy or spring potential energy.
01:20
Since there's no, since there's no, i'm going to put this at, this is going to be at point, let's say b, and this will be at point, let's just say a.
01:37
Okay.
01:39
Since there's not going to be any friction or anything else, we won't have any external work done on the system.
01:44
System, you know, the gravitational potential energy really isn't a thing for this because we're staying horizontal the whole time.
01:52
We're not changing a height value for this block spring system.
01:56
So really that's all we have is just the block.
01:59
We have the block and we have the spring in our system.
02:04
So what we can do just to model the relationship of energy here.
02:09
At b, this is where really just kind of like your normal, line is this is like your zero line for for uh you could say for dis for displacement um right here at zero is is the equilibrium position um and in order to understand the answer choices we need to understand the dynamics of what's happening here um with this system so this is the equilibrium position and it's at this position that we don't have any that the spring is not stretched so the spring is fully relaxed here.
03:00
So with the spring being fully relaxed, there's no spring energy or elastic potential energy.
03:08
All of the energy is in the form of, we would say, kinetic if this spring was moving around.
03:15
Let's pretend it is.
03:16
Let's pretend we squeezed it.
03:18
And we've caught it right here.
03:20
We froze time, and we saw that it was at b, but we know it was.
03:25
Moving when we froze this picture frame here of it being moving across the surface here.
03:31
We just kind of, you know, did a little frozen picture of here being at b.
03:37
We know that it had kinetic energy at b.
03:40
It was going to move past b.
03:42
Let's pretend it's on its way towards a.
03:45
So let me give a little velocity vector.
03:48
Even though the problem didn't say this.
03:49
I know we're just modeling some basics about what's happening.
03:53
So let's say that it's moving this direction towards a.
03:57
Well, when it gets over there to a, that's as scrunched up in this system as the spring will get.
04:03
And at that point, the block will stop moving on the spring.
04:08
It'll stop moving.
04:08
It's going to be getting ready to turn around.
04:10
So what we would say then is kinetic energy at that point, at point a is going to have no energy value.
04:17
And all of the energy is going to be, and i'm just choosing, i'm just choosing to do four little cubes of energy because i want to.
04:25
It doesn't, you could do five or two or whatever.
04:28
It doesn't matter.
04:30
But what we're saying here with this is that we're always saying that no matter how you look at this, the total energy on both sides, on both sides of the, wherever this thing, this block is at, is always equal to the total energy later.
04:45
So i'll put the total energy at point b, in this case, is equal to the total energy point a.
04:52
And if you did that, you would just basically say, well, that means that the kinetic energy at a plus the spring energy at a is equal to, i'm sorry, at the, let me fix that, is equal to the kinetic energy at a plus the potential energy, spring potential energy at a.
05:19
And obviously we know these are zeroed out here and here.
05:27
And so really, you just get a conservation equation here saying that the spring that the kinetic energy in the spring at b is equal to the spring potential energy at a and guess what that's what it would also equal even though we didn't show it we can assume that it's also what what the spring potential energy is at at c at c as well when it gets way over there the other side okay so um what we're basically saying here is energy is conserved again just going to roundabout way.
05:59
So if we get into your answer choices now, you know, which one of these is true.
06:05
If we got to start at the bottom, the potential energy of the system is never zero.
06:11
Well, we just showed at point b when it's at the equilibrium position and the spring is fully relaxed, there's no energy stored in that spring.
06:19
So there is no energy there.
06:21
It's zero because all of the energy in the system, in the block spring system is in the form of kinetic energy.
06:27
It's in the form of moving around.
06:30
So that can't be true.
06:33
Potential energy, the system is never zero.
06:34
Well, it is sometimes zero.
06:36
So that's not true.
06:38
And then if we go back a little bit more, starting, you know, go to the next one from the last.
06:44
It says the total energy of the oscillating system is lower than the mass, lower when the mass is at equilibrium position paired with the mass being at max amplitude...