00:01
So with this problem, we're given the scenario of a simple harmonic oscillator where there's a 0 .5 kilogram block attached to a spring.
00:09
The block slides back and forth over a frictionless surface, and it has an equilibrium point at position x equals zero.
00:18
At time equals zero, the block is at position zero, and then it starts off first moving in the positive direction.
00:28
And then we're given this graph here that shows both our position on our x -axis as well as the force, the magnitude of the net force on the block.
00:41
And we're seeing here that the force fs is equal, we're told, is equal to 75 newtons.
00:54
The first thing we're asked to figure out is what is the amplitude of this block.
01:00
So we want to find our amplitude, so our xm, and we can do that just by looking directly at the graph itself.
01:11
The amplitude is going to be where the block hits its maximum point, and if we follow that up from the graph, we can see that that is at position 0 .3 meters.
01:23
So our amplitude is just going to be 0 .30 meters.
01:30
The next thing we are asked to find is going to be our period.
01:36
So we're trying to find the period of the oscillation.
01:40
And we can do that.
01:42
If we start off with the equation, period equals 2 pi times the square root of mass divided by our our spring constant, we'll be able to find the period.
01:58
Now, the issue is we don't know our spring constant.
02:02
So we're going to have to actually take this term and substitute another equation in for that.
02:11
And we're going to, because we do know the force, we're going to use the equation, force equals negative kx and rearrange that for k.
02:22
So our k is.
02:23
So our k is.
02:24
Going to equal negative force divided by our position.
02:30
And again, looking up here at the graph, we can see that when we have our maximum force, we are also at our maximum position here.
02:38
So we can substitute in these values.
02:42
So we have a force of, or we have a k equals, k is going to equal negative 75 newtons divided by 0 .30 meters which gives us a k value of 250 newtons per meter and we can now take that and substitute that back in up here into our equation for our period so we have t equals 2 pi times the square root.
03:28
The mass of the block is 0 .5 0 kilograms.
03:33
Our k value is 250 newtons per meter, so we end up with a t value of t equals 0 .281 seconds...