00:01
Hello, today we're trying to solve for the natural resonance frequency of this system on the left, which is shown here in red, with the spring, with spring constant k and some mass am attached to it.
00:16
The question is, what is the natural resonance frequency in omega and f the frequency in hertz of this particular system? now the image that comes along with us tells us that the spring constant k is 54 pounds per inches and that the weight, not the mass, but the weight of the block is 64 .4 pounds.
00:39
And so we want to get these first into some nicer units, probably si units, something that we're more used to, so that we can use our calculations to find omega and f rather quickly.
00:50
So first let me convert k and w.
00:53
W, a cave that we first need to convert from 54 pounds per inch.
01:03
Here we go, and we know that one newton, which is the si unit that we should try and work in.
01:10
0 .2248 pounds in one newton.
01:15
And then inches, we want to get that into meters, so we want a meter.
01:20
And we know that there are 39 .3701 inches in a meter.
01:29
And if you calculate that in your calculator, you end up with 9 .456 .7 newtons per meter.
01:36
This is a more useful unit that we can actually use.
01:40
So next we need to convert the weight, and then we need to find the mass out of that weight.
01:45
So the weight, which i'm doing is a curly w so that we don't confuse it with omega.
01:50
Here is 64 .4 pounds.
01:55
Here again, we need to convert, and we use the same .2248 pounds and 1 newton.
02:03
When we do that, we end up with 286 .5 newton's.
02:10
Again, this is the weight, not the mass.
02:14
This is not the mass...